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Sample records for 3d yang-mills theory

  1. Gauged supersymmetries in Yang-Mills theory

    SciTech Connect

    Tissier, Matthieu; Wschebor, Nicolas

    2009-03-15

    In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.

  2. Gauged supersymmetries in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Tissier, Matthieu; Wschebor, Nicolás

    2009-03-01

    In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.

  3. Gravitino interactions from Yang-Mills theory

    SciTech Connect

    Bjerrum-Bohr, N. E. J.; Engelund, Oluf Tang

    2010-05-15

    We fabricate gravitino vertex interactions, using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory/gravity relations, aiming to achieve a better understanding of Kawai-Lewellen-Tye factorizations for gravitinos at an off-shell Lagrangian level. A useful by-product of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five-point scattering.

  4. Wong's equations in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Storchak, Sergey

    2014-04-01

    Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semi-simple Lie group are derived. The equations obtained are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations, we obtain Wong's equations in a pure Yang-Mills gauge theory with Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures performed in a finite-dimensional dynamical system and the reduction procedure in Yang-Mills gauge fields.

  5. Superstring limit of Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Lechtenfeld, Olaf; Popov, Alexander D.

    2016-11-01

    It was pointed out by Shifman and Yung that the critical superstring on X10 =R4 ×Y6, where Y6 is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on Σ2 ×R2, where Σ2 is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on R2 ⊂Σ2 ×R2 with a moduli space X10. When the moduli of slowly moving thin vortices depend on the coordinates of Σ2, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on Σ2 × Tp2, where Tp2 is a two-dimensional torus with a puncture p. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on Tp2, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.

  6. Perturbative spacetimes from Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.

    2017-04-01

    The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

  7. Quantum Yang-Mills field theory

    NASA Astrophysics Data System (ADS)

    Frasca, Marco

    2017-01-01

    We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.

  8. Band structure in Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Bachas, Constantin; Tomaras, Theodore

    2016-05-01

    We show how Yang-Mills theory on S3 × ℝ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different θ sectors coexist and are only mixed by (non-local) volume operators. Our analysis sheds light on, and extends Seiberg's proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that B + L violation at LHC is unsuppressed.

  9. Knot Theory and Topologically Massive Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Yildirim, Tuna; Rodgers, Vincent; Nair, Parameswaran; Carter, Suzanne

    2013-04-01

    In 2+1 dimensions, we study Yang-Mills(YM) + Chern-Simons(CS) theory also known as topologically massive Yang-Mills(TMYM) theory. Using geometric quantization method we calculate the Wilson Loop expectation values of TMYM theory. At large distances, where only the topological theory survives, we obtain a condition that makes skein relations of knot theory useful to calculate Wilson loop expectation values of TMYM theory. These link invariants may lead to a better understanding of mass gap in 2+1 dimensions.

  10. Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory

    NASA Astrophysics Data System (ADS)

    Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito

    2015-01-01

    We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.

  11. Einstein-Yang-Mills theory: Asymptotic symmetries

    NASA Astrophysics Data System (ADS)

    Barnich, Glenn; Lambert, Pierre-Henry

    2013-11-01

    Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.

  12. Path integral regularization of pure Yang-Mills theory

    SciTech Connect

    Jacquot, J. L.

    2009-07-15

    In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.

  13. Instanton Effective Action in Deformed Super Yang-Mills Theories

    SciTech Connect

    Nakajima, Hiroaki; Ito, Katsushi; Sasaki, Shin

    2008-11-23

    We study the ADHM construction of instantons in N = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C{sup 2}/Z{sub 2} in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with spacetime dependent gauge coupling such that the action reproduces the effective action of the fractional branes.

  14. Twin supergravities from Yang-Mills theory squared

    NASA Astrophysics Data System (ADS)

    Anastasiou, A.; Borsten, L.; Duff, M. J.; Hughes, M. J.; Marrani, A.; Nagy, S.; Zoccali, M.

    2017-07-01

    We consider "twin supergravities"—pairs of supergravities with N+ and N- supersymmetries, N+>N-, with identical bosonic sectors—in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old ones. In particular, the matter coupled N- twins in D =3 , 5, 6 and the N-=1 twins in D =4 have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bifundamental scalar that couples to the well-known biadjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorization into left and right super Yang-Mills-matter theories.

  15. Full colour for loop amplitudes in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Ochirov, Alexander; Page, Ben

    2017-02-01

    We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, JHEP 10 (2015) 064. In this note, we give a careful exposition of the method and discuss its connection to looplevel Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.

  16. Field-dependent BRST transformations in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Lavrov, Peter M.; Lechtenfeld, Olaf

    2013-10-01

    We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary Rξ gauges.

  17. Perturbation Theory of Massive Yang-Mills Fields

    DOE R&D Accomplishments Database

    Veltman, M.

    1968-08-01

    Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

  18. Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Kotanski, J.

    2008-12-01

    The main features of the cusp anomalous dimension in N=4 supersymmetric Yang-Mills theory are reviewed. Moreover, the strong coupling expansion of the cusp derived in B. Basso, G.P. Korchemsky, J. Kotanski, Phys. Rev. Lett. 100, 091601 (2008) is presented.

  19. Hamiltonian flow in Coulomb gauge Yang-Mills theory

    SciTech Connect

    Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel

    2011-01-15

    We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.

  20. Deconfinement in Yang-Mills Theory through Toroidal Compactification

    SciTech Connect

    Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC

    2011-08-12

    We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.

  1. Infrared propagators of Yang-Mills theory from perturbation theory

    SciTech Connect

    Tissier, Matthieu; Wschebor, Nicolas

    2010-11-15

    We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the peculiarities of the propagators in d=2.

  2. Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Endres, Michael G.; Brower, Richard C.; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V.

    2015-12-01

    We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.

  3. SL(2, r) Yang-Mills Theory on a Circle

    NASA Astrophysics Data System (ADS)

    Bengtsson, Ingemar; Hallin, Joakim

    The kinematic of SL(2, ℝ) Yang-Mills theory on a circle is considered, for reasons that are spelt out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff “network” topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case and cannot be resolved through the kind of appeal made to group theory in that case.

  4. Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory

    NASA Astrophysics Data System (ADS)

    Gross, David

    David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...

  5. Saddle-point solutions in Yang-Mills-dilaton theory

    NASA Astrophysics Data System (ADS)

    Bizon, Piotr

    1993-02-01

    The coupling of a dilaton to the SU(2)-Yang-Mills field leads to interesting nonperturbative static spherically symmetric solutions which are studied by mixed analytical and numerical methods. In the Abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the non-Abelian sector there exists a countable family of globally regular solutions which are purely magnetic but have a zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the Abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with an increasing number of unstable modes. The existence and instability of these solutions are ``explained'' by the Morse-theory argument recently proposed by Sudarsky and Wald.

  6. Saddle-point solutions in Yang-Mills--dilaton theory

    SciTech Connect

    Bizon, P. )

    1993-02-15

    The coupling of a dilaton to the SU(2)-Yang-Mills field leads to interesting nonperturbative static spherically symmetric solutions which are studied by mixed analytical and numerical methods. In the Abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the non-Abelian sector there exists a countable family of globally regular solutions which are purely magnetic but have a zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the Abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with an increasing number of unstable modes. The existence and instability of these solutions are explained'' by the Morse-theory argument recently proposed by Sudarsky and Wald.

  7. Currents and anomalies in topological Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Dahmen, H. D.; Marculescu, S.; Szymanowski, L.

    1992-09-01

    The quantum properties of topological Yang-Mills theory are investigated in the light of the N = 2 supersymmetry observed in flat space. We construct a unique system of covariantly (partially) conserved currents which develop anomalies while preserving BRS invariance of the theory. In particular, the one-loop renormalized energy-momentum tensor is free of purely gravitational contributions and can be written as a BRS variation. We study the consequences of changing the renormalization prescriptions inherited from the N = 2 supersymmetry to those consistent with BRS. Most of our conclusions are verified by explicit calculations. As a byproduct we derive the formula of Atiyah, Hitchin and Singer for the dimension of the moduli space of self-dual Yang-Mills fields. Finally strong arguments are given that the full system of Donaldson polynomials and the quantum BRS current are not renormalized beyond one-loop.

  8. On matrix model formulations of noncommutative Yang-Mills theories

    SciTech Connect

    Azeyanagi, Tatsuo; Hirata, Tomoyoshi; Hanada, Masanori

    2008-11-15

    We study the stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to the noncommutative Yang-Mills theories. It turns out that most noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R{sup D} pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic noncommutative Yang-Mills theories are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.

  9. Compactification driven hilltop inflation in Einstein-Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Ó Colgáin, Eoin; Zaballa, Ignacio

    2010-04-01

    Starting from Einstein-Yang-Mills theory in higher dimensions with an instanton on a compact sphere, we dimensionally reduce to find an effective four-dimensional action describing “hilltop” inflation. Using recent CMB data, we analyze the parameter space of this model to search for viable setups. One unique feature of this class of inflationary models is that the value of the inflaton field, or alternatively, the size of the compact sphere, is stabilized dynamically during the inflationary process.

  10. Topological susceptibility for the SU(3) Yang Mills theory

    NASA Astrophysics Data System (ADS)

    Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio

    2005-03-01

    We present the results of a computation of the topological susceptibility in the SU(3) Yang-Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r04χ=0.059(3), which corresponds to χ=(191 if F K is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the η.

  11. Unification of Yang-Mills theory and superstrings

    SciTech Connect

    Chapline, G.F. )

    1988-01-01

    A scheme is suggested for constructing new types of superstrings with critical dimensions D = 10 and D = 26 by introducing Yang-Mills potentials as auxiliary fields. The Yang-Mills gauge group is fixed by the critical dimensions and the requirement that it must be spontaneously broken in order that the conformal anomaly cancel. For critical dimension D = 26 a superstring may exist with an unbroken SU(3) X SU(2) X U(1) gauge invariance. This superstring has N = 2 supersymmetry and is constrained to move on a nontrivial 24-dimensional complex manifold. Both the first quantized and second quantized versions of these string theories give promise of an interesting mathematical interpretation.

  12. Asymptotic symmetries of Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Strominger, Andrew

    2014-07-01

    Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.

  13. Yang-Mills theories at high energy accelerators

    NASA Astrophysics Data System (ADS)

    Sterman, George

    2016-03-01

    I will begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.

  14. Ward identity implies recursion relations in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Chen, Gang

    2012-07-01

    The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.

  15. Width of the confining string in Yang-Mills theory.

    PubMed

    Gliozzi, F; Pepe, M; Wiese, U-J

    2010-06-11

    We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.

  16. Counting the massive vacua of super Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Bourget, Antoine; Troost, Jan

    2015-08-01

    We compute the number of massive vacua of supersymmetric Yang-Mills theory on mass-deformed to preserve supersymmetry, for any gauge group G. We use semi-classical techniques and efficiently reproduce the known counting for A, B and C type gauge groups, present the generating function for both O(2 n) and SO(2 n), and compute the supersymmetric index for gauge groups of exceptional type. A crucial role is played by the classification of nilpotent orbits, as well as global properties of their centralizers. We give illustrative examples of new features of our analysis for the D-type algebras.

  17. Transport coefficients in Yang-Mills theory and QCD.

    PubMed

    Christiansen, Nicolai; Haas, Michael; Pawlowski, Jan M; Strodthoff, Nils

    2015-09-11

    We calculate the shear-viscosity-over-entropy-density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently, we provide a first estimate for η/s in QCD.

  18. MONOPOLES AND DYONS IN THE PURE EINSTEIN YANG MILLS THEORY

    SciTech Connect

    HOSOTANI,Y.; BJORAKER,J.

    1999-08-16

    In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. In asymptotically anti-de Sitter space a class of monopole solutions have no node in non-Abelian magnetic fields, and are stable against spherically symmetric perturbations.

  19. Emergent Yang-Mills theories from universal extra dimensions

    NASA Astrophysics Data System (ADS)

    Chkareuli, J. L.; Kepuladze, Z.

    2017-02-01

    We study emergent Yang-Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang-Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.

  20. Boundary effects in super-Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Shah, Mushtaq B.; Faizal, Mir; Ganai, Prince A.; Zaz, Zaid; Bhat, Anha; Masood, Syed

    2017-05-01

    In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this N = 2 Yang-Mills theory with a boundary.

  1. Confinement in a three-dimensional Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Frasca, Marco

    2017-04-01

    We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.

  2. Resurgence, operator product expansion, and remarks on renormalons in supersymmetric Yang-Mills theory

    SciTech Connect

    Shifman, M.

    2015-03-15

    We discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In N = 1 super-Yang-Mills theories, renormalons are peculiar and are not quite similar to renormalons in QCD.

  3. Lifting the Gribov ambiguity in Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Serreau, J.; Tissier, M.

    2012-05-01

    We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.

  4. Super Yang-Mills theory as a random matrix model

    SciTech Connect

    Siegel, W.

    1995-07-15

    We generalize the Gervais-Neveu gauge to four-dimensional {ital N}=1 superspace. The model describes an {ital N}=2 super Yang-Mills theory. All chiral superfields ({ital N}=2 matter and ghost multiplets) exactly cancel to all loops. The remaining Hermitian scalar superfield (matrix) has a renormalizable massive propagator and simplified vertices. These properties are associated with {ital N}=1 supergraphs describing a superstring theory on a random lattice world sheet. We also consider all possible finite matrix models, and find they have a universal large-color limit. These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.

  5. Covariant variational approach to Yang-Mills theory: Thermodynamics

    NASA Astrophysics Data System (ADS)

    Quandt, M.; Reinhardt, H.

    2017-09-01

    The thermodynamics of S U (2 ) Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a nontrivial Polyakov loop to the pressure of the gluon plasma. The Poisson resummed expression for the pressure can be evaluated analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at T →∞ , while the limit T →0 is afflicted by artifacts due to massless modes in the confined phase. Several remedies to remove these artifacts are discussed. Using the numerical T =0 solutions for the ghost and gluon propagators in the covariant variational approach as input, the pressure, energy density and interaction strength are calculated and compared to lattice data.

  6. Yang-Mills gauge theory and Higgs particle

    NASA Astrophysics Data System (ADS)

    Wu, Tai Tsun; Wu, Sau Lan

    2015-12-01

    Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU(2) × SU(3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.

  7. Yang-Mills Gauge Theory and Higgs Particle

    NASA Astrophysics Data System (ADS)

    Wu, Tai Tsun; Wu, Sau Lan

    Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU (2) × SU (3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.

  8. Is the ground state of Yang-Mills theory Coulombic?

    SciTech Connect

    Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.; Lutz, W.

    2008-08-01

    We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.

  9. Residual Confinement in High-Temperature Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Maas, A.; Wambach, J.; Grüter, B.; Alkofer, R.

    2005-01-01

    The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.

  10. Thermal Yang-Mills theory in the Einstein universe

    NASA Astrophysics Data System (ADS)

    Avramidi, Ivan G.; Collopy, Samuel

    2012-09-01

    We study the stability of a non-Abelian chromomagnetic vacuum in Yang-Mills theory in Euclidean Einstein universe S1 × S3. We assume that the gauge group is a simple compact group G containing the group SU(2) as a subgroup and consider static covariantly constant gauge fields on S3 taking values in the adjoint representation of the group G and forming a representation of the group SU(2). We compute the heat kernel for the Laplacian acting on fields on S3 in an arbitrary representation of SU(2) and use this result to compute the heat kernels for the gluon and the ghost operators and the one-loop effective action. We show that the only configuration of the covariantly constant Yang-Mills background that is stable is the one that contains only spinor (fundamental) representations of the group SU(2); all other configurations contain negative modes and are unstable. For the stable configuration we compute the asymptotics of the effective action, the energy density, the entropy and the heat capacity in the limits of low/high temperature and small/large volume and show that the energy density has a non-trivial minimum at a finite value of the radius of the sphere S3. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

  11. Non-uniqueness of quantized Yang - Mills theories

    NASA Astrophysics Data System (ADS)

    Dütsch, Michael

    1996-12-01

    We consider quantized Yang - Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant to first order contains a two-parametric ambiguity in the ghost sector: a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are also gauge invariant. Moreover, we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of the divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the simplest one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proved for all orders.

  12. Infrared singularities in Landau gauge Yang-Mills theory

    SciTech Connect

    Alkofer, Reinhard; Huber, Markus Q.; Schwenzer, Kai

    2010-05-15

    We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.

  13. Composite strings in (2+1)-dimensional anisotropic weakly coupled Yang-Mills theory

    SciTech Connect

    Orland, Peter

    2008-01-15

    The small-scale structure of a string connecting a pair of static sources is explored for the weakly coupled anisotropic SU(2) Yang-Mills theory in (2+1) dimensions. A crucial ingredient in the formulation of the string Hamiltonian is the phenomenon of color smearing of the string constituents. The quark-antiquark potential is determined. We close with some discussion of the standard, fully Lorentz-invariant Yang-Mills theory.

  14. Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory

    SciTech Connect

    Kondo, Kei-Ichi; Shibata, Akihiro; Shinohara, Toru; Kato, Seikou

    2012-10-23

    We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.

  15. Mapping a Massless Scalar Field Theory on a Yang-Mills Theory:. Classical Case

    NASA Astrophysics Data System (ADS)

    Frasca, Marco

    We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.

  16. Surface-invariants in 2D classical Yang-Mills theory

    SciTech Connect

    Diaz, Rafael; Fuenmayor, E.; Leal, Lorenzo

    2006-03-15

    We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to nondynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on-shell action, which are area-invariants. A geometrical interpretation of these invariants is given.

  17. A quantization of twistor Yang-Mills theory through the background field method

    NASA Astrophysics Data System (ADS)

    Boels, Rutger

    2007-11-01

    Four-dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between textbook perturbation theory and the Cachazo-Svrček-Witten rules. In this paper we study nonsupersymmetric twistor Yang-Mills theory at loop level using the background field method. For an appropriate partial quantum field gauge choice it is shown that the calculation of the effective action is equivalent to (the twistor lift of) the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel formulation to all orders in perturbation theory. A direct consequence is that the twistor version of Yang-Mills theory is just as renormalizable in this particular gauge. As applications an explicit calculation of the Yang-Mills beta function and some preliminary investigations into using the formalism to calculate S-matrix elements at loop level are presented. In principle the technique described in this paper generates consistent quantum completions of the Cachazo-Svrček-Witten rules. However, by inherent limitations of the partial gauge choice employed here, this offers in its current form mainly simplifications for tree-level forestry. The method is expected to be applicable to a wide class of four-dimensional gauge theories.

  18. Supersymmetric Yang-Mills theory as higher Chern-Simons theory

    NASA Astrophysics Data System (ADS)

    Sämann, Christian; Wolf, Martin

    2017-07-01

    We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.

  19. Topological Geon Black Holes in Einstein-Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Kottanattu, George T.; Louko, Jorma

    2011-04-01

    We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle's static, spherically symmetric SU( n) black holes with n > 2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz's static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon's gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.

  20. Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice

    SciTech Connect

    Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru; Kato, Seikou

    2016-01-22

    In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the “Abelian” dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.

  1. Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Kato, Seikou; Shinohara, Toru

    2016-01-01

    In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.

  2. Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge--Revisited

    SciTech Connect

    Reinhardt, Hugo; Campagnari, Davide R.; Leder, Markus; Burgio, Giuseppe; Quandt, Markus; Pawlowski, Jan M.; Weber, Axel

    2011-05-24

    I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang-Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.

  3. Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

    SciTech Connect

    Campagnari, Davide R.; Reinhardt, Hugo; Weber, Axel

    2009-07-15

    We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static color sources are calculated to one-loop order. Furthermore, the one-loop {beta} function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.

  4. Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies

    NASA Astrophysics Data System (ADS)

    Hofmann, Ralf

    2014-04-01

    A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (anti)selfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anti)calorons of scale parameter ρ ˜ |φ|-1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anti)caloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anti)caloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in

  5. Center-stabilized Yang-Mills Theory:Confinement and Large N Volume Independence

    SciTech Connect

    Unsal, Mithat; Yaffe, Laurence G.; /Washington U., Seattle

    2008-03-21

    We examine a double trace deformation of SU(N) Yang-Mills theory which, for large N and large volume, is equivalent to unmodified Yang-Mills theory up to O(1/N{sup 2}) corrections. In contrast to the unmodified theory, large N volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large N volume independence in small volumes. For small values of N, if the theory is formulated on R{sup 3} x S{sup 1} with a sufficiently small compactification size L, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference L or number of colors N decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small N the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large N it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.

  6. Three Proofs of the Makeenko-Migdal Equation for Yang-Mills Theory on the Plane

    NASA Astrophysics Data System (ADS)

    Driver, Bruce K.; Hall, Brian C.; Kemp, Todd

    2017-04-01

    We give three short proofs of the Makeenko-Migdal equation for the Yang-Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular, our proofs are "local" in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with Gabriel, we show that two of our proofs can be adapted to the case of Yang-Mills theory on any compact surface.

  7. Hamilton-Jacobi treatment of QED and Yang-Mills theory as constrained systems

    SciTech Connect

    Rabei, E.M.; Tawfiq, S.

    1997-06-01

    The QED and Yang-Mills theories are treated as constrained systems using the Hamilton-Jacobi approach. The set of Hamilton-Jacobi partial differential equations of these theories is obtained. It is shown that their simultaneous solutions lead to the original action without introducing Lagrange multipliers.

  8. Covariant gauges without Gribov ambiguities in Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Serreau, J.; Tissier, M.; Tresmontant, A.

    2014-06-01

    We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.

  9. Off-shell invariant D = N = 2 twisted super Yang-Mills theory with a gauged central charge without constraints

    NASA Astrophysics Data System (ADS)

    Asaka, Keisuke; Kato, Junji; Kawamoto, Noboru; Miyake, Akiko

    2013-11-01

    We formulate N=2 twisted super Yang-Mills theory with a gauged central charge by superconnection formalism in two dimensions. We obtain off-shell invariant supermultiplets and actions with and without constraints, which is in contrast with the off-shell invariant D=N=4 super Yang-Mills formulation with unavoidable constraints.

  10. Numerical simulations of dynamical gluinos in SU (3) Yang-Mills theory: first results

    NASA Astrophysics Data System (ADS)

    Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, István; Münster, Gernot; DESY-Münster Collaboration

    In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.

  11. Evidence for discrete chiral symmetry breaking in N=1 supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Desy-Münster Collaboration; Kirchner, R.; Montvay, I.; Westphalen, J.; Luckmann, S.; Spanderen, K.

    1999-01-01

    In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking Z4-->Z2 caused by gaugino condensation.

  12. The Makeenko-Migdal Equation for Yang-Mills Theory on Compact Surfaces

    NASA Astrophysics Data System (ADS)

    Driver, Bruce K.; Gabriel, Franck; Hall, Brian C.; Kemp, Todd

    2017-06-01

    We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.

  13. Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory at Strong Coupling

    SciTech Connect

    Basso, B.; Korchemsky, G. P.; Kotanski, J.

    2008-03-07

    We construct an analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high-spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.

  14. Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge

    SciTech Connect

    Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel

    2011-05-23

    A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.

  15. Perturbative Quantum Gravity and Yang-Mills Theories in de Sitter Spacetime

    NASA Astrophysics Data System (ADS)

    Faizal, Mir

    2011-05-01

    This thesis consists of three parts. In the first part we review the quantization of Yang-Mills theories and perturbative quantum gravity in curved spacetime. In the second part we calculate the Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge. In the third part we investigate the physical equivalence of covariant Wightman graviton two-point function with the physical graviton two-point function. The Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, that if we regularize these divergences by introducing a finite mass and take the zero mass limit at the end, then the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. We thus find effective Feynman propagators for ghosts in Yang-Mills theories and perturbative quantum gravity by subtracting out these divergent modes. It is known that the covariant graviton two-point function in de Sitter spacetime is infrared divergent for some choices of gauge parameters. On the other hand it is also known that there are no infrared problems for the physical graviton two-point function obtained by fixing all gauge degrees of freedom, in global coordinates. We show that the covariant Wightman graviton two-point function is equivalent to the physical one in the sense that they result in the same two-point function of any local gauge-invariant quantity. Thus any infrared divergence in the Wightman graviton two-point function in de Sitter spacetime can only be an gauge artefact.

  16. Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory

    SciTech Connect

    Ydri, Badis

    2007-05-15

    We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two plaquettes. This equivalence holds in the 'fuzzy sphere' phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the matrix phase we have a U(N) gauge theory on a single point.

  17. Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Mafra, Carlos R.; Schlotterer, Oliver

    2015-09-01

    In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.

  18. Non-Abelian Dual Superconductivity in SU(3) Yang-Mills Theory due to Non-Abelian Magnetic Monopoles

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi; Shibata, Akihiro; Kato, Seikou; Shinohara, Toru

    We give numerical evidences for the non-Abelian dual superconductivity due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory as a mechanism for quark confinement, based on our new formulation of lattice gauge theory.

  19. Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

    SciTech Connect

    Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; Detmold, William; Pochinsky, Andrew V.

    2015-12-29

    In this study, we present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.

  20. Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

    DOE PAGES

    Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; ...

    2015-12-29

    In this study, we present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.

  1. Amplitude relations in heterotic string theory and Einstein-Yang-Mills

    NASA Astrophysics Data System (ADS)

    Schlotterer, Oliver

    2016-11-01

    We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension α' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.

  2. Hedgehogs in Wilson loops and phase transition in SU(2) Yang Mills theory

    NASA Astrophysics Data System (ADS)

    Belavin, V. A.; Chernodub, M. N.; Kozlov, I. E.

    2006-08-01

    We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these "hedgehog loops" are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.

  3. Towards the Finite Temperature Gluon Propagator in Landau Gauge Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Maas, A.

    2003-12-01

    Yang-Mills theories undergo a deconfining phase transition at a critical temperature. In lattice calculations the temporal Wilson loop and. Z3 order parameter show above this temperature a behavior typical of deconfinement. A quantity of interest in the study of this transition is the gluon propagator and its evolution with temperature. This contribution describes the current status of an investigation of the finite temperature gluon propagator in Landau gauge. It analyzes the high temperature case. The resulting equations are compared to the corresponding ones of three-dimensional Yang-Mills theory. Under certain assumptions it is found that a kind of spatial "confinement" is still present, even at very high temperatures.

  4. Quantum Metamorphosis of a Conformal Transformation in D3-Brane Yang-Mills Theory

    SciTech Connect

    Jevicki, A.; Kazama, Y.; Yoneya, T.

    1998-12-01

    We show how the linear special conformal transformation in four-dimensional N=4 super-Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti{endash}de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS{sub 5}{times} S{sup 5} supergravity and super-Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence. {copyright} {ital 1998} {ital The American Physical Society}

  5. Tree amplitudes of noncommutative U(N) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Huang, Jia-Hui; Huang, Rijun; Jia, Yin

    2011-10-01

    Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation.

  6. Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.

    PubMed

    Brandhuber, Andreas; Penante, Brenda; Travaglini, Gabriele; Young, Donovan

    2015-02-20

    We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of N=4 supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions.

  7. On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Nolan, Brien C.; Winstanley, Elizabeth

    2016-02-01

    We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

  8. Topological String Models for the Generalized Two-Dimensional Yang-Mills Theories

    NASA Astrophysics Data System (ADS)

    Sugawara, Y.

    1996-06-01

    We discuss some aspects of the large N expansions of the generalized two-dimensional Yang-Mills theories (gYM2), and especially, clarify the geometrical meanings of the higher Casimirs. Based on these results we attempt to extend the Cordes-Moore-Ramgoolam topological string model describing the ordinary YM2 to those describing gYM2. The concept of ``deformed gravitational descendants'' will be introduced for this purpose.

  9. Four-loop dressing phase of N=4 super-Yang-Mills theory

    SciTech Connect

    Beisert, N.; McLoughlin, T.; Roiban, R.

    2007-08-15

    We compute the dilatation generator in the su(2) sector of planar N=4 super-Yang-Mills theory at four loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed directly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to {zeta}(3)

  10. Yang-Mills theory at 60: Milestones, landmarks and interesting questions

    NASA Astrophysics Data System (ADS)

    Chau, Ling-Lie

    2015-12-01

    On the auspicious occasion of celebrating the 60th anniversary of the Yang-Mills theory, and Professor Yang’s many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that still lie before us. The paper is written (without equations) for the interest of non-scientists as well as of scientists.

  11. On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

    NASA Astrophysics Data System (ADS)

    Bassetto, Antonio; DePol, Giancarlo; Torrielli, Alessandro; Vian, Federica

    2005-05-01

    We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.

  12. Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling

    SciTech Connect

    Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro

    2010-05-28

    We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.

  13. Euclidean wormhole solutions of Einstein-Yang-Mills theory in diverse dimensions

    SciTech Connect

    Yoshida, K.; Hirenzaki, S. ); Shiraishi, K. )

    1990-09-15

    We solve the Euclidean Einstein equations with non-Abelian gauge fields of sufficiently large symmetry in various dimensions. In higher-dimensional spaces, we find the solutions which are similar to so-called scalar wormholes. In four-dimensional space-time, we find singular wormhole solutions with infinite Euclidean action. Wormhole solutions in the three-dimensional Einstein-Yang-Mills theory with a Chern-Simons term are also constructed.

  14. Solving the ghost-gluon system of Yang-Mills theory on GPUs

    NASA Astrophysics Data System (ADS)

    Hopfer, Markus; Alkofer, Reinhard; Haase, Gundolf

    2013-04-01

    We solve the ghost-gluon system of Yang-Mills theory using graphics processing units (GPUs). Working in the Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description, as this approach is well suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA™. Our results show that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.

  15. Boundary behaviors for general off-shell amplitudes in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Zhang, Yun; Chen, Gang

    2013-07-01

    The boundary behavior of amplitudes—the amplitudes’ behavior under a large Britto-Cachazo-Feng-Witten (BCFW) momenta deformation for a pair of legs—in Yang-Mills theory is of great interest recently. In this article we analyze the boundary behavior of off-shell Yang-Mills amplitudes in Feynman gauge. The deformed legs can be either adjacent or nonadjacent. We find that a set of reduced vertices can be used to simplify the analysis and calculation of the boundary behavior of amplitudes. Boundary behavior for amplitudes with adjacent BCFW deformation is read off from the reduced vertices. Then we discover a relationship between a permutation sum with fixed color ordering of the legs and the improved boundary behavior for the off-shell amplitudes with a nonadjacent BCFW momenta deformation. Based on the boundary behavior, we generalize the BCFW recursion relation to calculate general tree-level off-shell amplitudes and analyze the relations between them.

  16. Center-symmetric effective theory for high-temperature SU(2) Yang-Mills theory

    SciTech Connect

    Forcrand, Ph. de; Kurkela, A.; Vuorinen, A.

    2008-06-15

    We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using nonperturbative lattice simulations. We find that at lower temperature the theory undergoes a second-order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry.

  17. Wilson punctured network defects in 2D q-deformed Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Watanabe, Noriaki

    2016-12-01

    In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU( N ) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.

  18. Renormalization of SU(2) Yang-Mills theory with flow equations

    NASA Astrophysics Data System (ADS)

    Efremov, Alexander N.; Guida, Riccardo; Kopper, Christoph

    2017-09-01

    We give a proof of perturbative renormalizability of SU(2) Yang-Mills theory in four-dimensional Euclidean space which is based on the flow equations of the renormalization group. The main motivation is to present a proof which does not make appear mathematically undefined objects (as, for example, dimensionally regularized generating functionals), which permits to parametrize the theory in terms of physical renormalization conditions, and which allows to control the singularities of the correlation functions of the theory in the infrared domain. Thus a large part of the proof is dedicated to bounds on massless correlation functions.

  19. Quantization of Yang-Mills theory without the Gribov ambiguity

    NASA Astrophysics Data System (ADS)

    Zhou, Gao-Liang; Yan, Zheng-Xin; Zhang, Xin

    2017-03-01

    A gauge fixing condition is presented here for non-Abelian gauge theory on the manifold R ⊗S1 ⊗S1 ⊗S1. It is proved that the new gauge fixing condition is continuous and free from the Gribov ambiguity. While perturbative calculations based on the new gauge condition behave like those based on the axial gauge in ultraviolet region, infrared behaviours of the perturbative series under the new gauge fixing condition are quite nontrivial. The new gauge condition, which reads n ṡ ∂ n ṡ A = 0, may not satisfy the boundary condition Aμ (∞) = 0 as required by conventional perturbative calculations for gauge theories on the manifold S4. However, such contradiction is not harmful for the theory considered here.

  20. Amplitudes in N = 4 Super-Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Spradlin, Marcus

    These lecture notes provide a lightning introduction to some aspects of scattering amplitudes in maximally supersymmetric theory, aimed at the audience of students attending the 2014 TASI summer school "Journeys Through the Precision Frontier: Amplitudes for Colliders". Emphasis is placed on explaining modern terminology so that students needing to delve further may more easily access the available literature.

  1. From SL(5, ℝ) Yang-Mills theory to induced gravity

    NASA Astrophysics Data System (ADS)

    Assimos, T. S.; Pereira, A. D.; Santos, T. R. S.; Sobreiro, R. F.; Tomaz, A. A.; Otoya, V. J. Vasquez

    From pure Yang-Mills action for the SL(5, ℝ) group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein-Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.

  2. Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.

    PubMed

    Zohar, Erez; Cirac, J Ignacio; Reznik, Benni

    2013-03-22

    Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.

  3. Reformulations of the Yang-Mills theory toward quark confinement and mass gap

    SciTech Connect

    Kondo, Kei-Ichi; Shinohara, Toru; Kato, Seikou; Shibata, Akihiro

    2016-01-22

    We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.

  4. Reformulations of the Yang-Mills theory toward quark confinement and mass gap

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

    2016-01-01

    We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N- 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1)N-1, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.

  5. From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.

    PubMed

    Pepe, M; Wiese, U-J

    2009-05-15

    We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.

  6. FIFTY YEARS OF YANG-MILLS THEORIES: A Phenomenological Point of View

    NASA Astrophysics Data System (ADS)

    de Rújula, Alvaro

    On the occasion of the celebration of the first half-century of Yang-Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds form nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.

  7. Nonperturbative gluon and ghost propagators for d=3 Yang-Mills theory

    SciTech Connect

    Aguilar, A. C.; Binosi, D.; Papavassiliou, J.

    2010-06-15

    We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in d=3 Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in d=3), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of SU(2) lattice simulations.

  8. Z{sub 2} monopoles in SU(n) Yang-Mills-Higgs theories

    SciTech Connect

    Kneipp, Marco A. C.; Liebgott, Paulo J.

    2010-02-15

    Z{sub n} monopoles are important for the understanding of the Goddard-Nuyts-Olive duality when the scalar field is not in the adjoint representation. We analyze the Z{sub 2} monopole solutions in SU(n) Yang-Mills-Higgs theories spontaneously broken to Spin(n)/Z{sub 2} by a scalar in the nxn representation. We construct explicitly Z{sub 2} monopole asymptotic fields solutions for each of the weights of the defining representation of the dual algebra so(n){sup or.}

  9. Nonsingular and accelerated expanding universe from effective Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    De Lorenci, Vitorio A.

    2010-03-01

    The energy-momentum tensor coming from one-parameter effective Yang-Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is examined. Particularly, it is shown that only solutions corresponding to an open model allow the universe to evolve into an accelerated expansion. This result appears as a possible mechanism for an inflationary phase produced by a vector field. Further, depending on the value of some parameters characterizing the system, the resulting models are classified as singular or nonsingular.

  10. Reformulations of Yang-Mills theories with space-time tensor fields

    NASA Astrophysics Data System (ADS)

    Guo, Zhi-Qiang

    2016-01-01

    We provide the reformulations of Yang-Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loop approximation.

  11. Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory

    SciTech Connect

    Kanamori, Issaku

    2009-06-01

    We measure the vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory using lattice simulation. The obtained vacuum energy density is E{sub 0}=0.09(9)((+10/-8))g{sup 2}, where the first error is the systematic and the second is the statistical one, measured in the dimensionful gauge coupling g which governs the scale of the system. The result is consistent with unbroken supersymmetry, although we cannot exclude a possible very small nonzero vacuum energy.

  12. Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling

    SciTech Connect

    Dixon, Lance J.; /SLAC

    2008-03-25

    I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.

  13. D=5 maximally supersymmetric Yang-Mills theory diverges at six loops

    NASA Astrophysics Data System (ADS)

    Bern, Zvi; Carrasco, John Joseph M.; Dixon, Lance J.; Douglas, Michael R.; von Hippel, Matt; Johansson, Henrik

    2013-01-01

    The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large Nc) maximally supersymmetric Yang-Mills theory in D=5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L>6 in the critical dimension D=4+6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.

  14. More on Gribov copies and propagators in Landau-gauge Yang-Mills theory

    SciTech Connect

    Maas, Axel

    2009-01-01

    Fixing a gauge in the nonperturbative domain of Yang-Mills theory is a nontrivial problem due to the presence of Gribov copies. In particular, there are different gauges in the nonperturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal Landau gauge and the absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, the finite-volume effects are also modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.

  15. Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery

    NASA Astrophysics Data System (ADS)

    Mansfield, Paul

    1994-04-01

    We solve Schrödinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero.

  16. Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space

    NASA Astrophysics Data System (ADS)

    Gorsky, A.

    2009-12-01

    We discuss multiloop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures which are the playgrounds for the Kodaira-Spencer or Kahler type gravity. We suggest fermionic representation of the loop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory assuming the identification of the IR regulator branes with Kodaira-Spencer fermions in the B model and Lagrangian branes in the A model. The two-easy mass box diagram is related to the correlator of fermionic currents on the spectral curve in the B model or hyperbolic volume in the A model and it plays the role of a building block in the whole picture. The Bern-Dixon-Smirnov-like ansatz has the interpretation as the semiclassical limit of a fermionic correlator. It is argued that fermionic representation implies a kind of integrability on the moduli spaces. We conjecture the interpretation of the reggeon degrees of freedom in terms of the open strings stretched between the IR regulator branes.

  17. Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space

    SciTech Connect

    Gorsky, A.

    2009-12-15

    We discuss multiloop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures which are the playgrounds for the Kodaira-Spencer or Kahler type gravity. We suggest fermionic representation of the loop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory assuming the identification of the IR regulator branes with Kodaira-Spencer fermions in the B model and Lagrangian branes in the A model. The two-easy mass box diagram is related to the correlator of fermionic currents on the spectral curve in the B model or hyperbolic volume in the A model and it plays the role of a building block in the whole picture. The Bern-Dixon-Smirnov-like ansatz has the interpretation as the semiclassical limit of a fermionic correlator. It is argued that fermionic representation implies a kind of integrability on the moduli spaces. We conjecture the interpretation of the reggeon degrees of freedom in terms of the open strings stretched between the IR regulator branes.

  18. Supersymmetric self-dual Yang-Mills theories from local nilpotent fermionic symmetry

    NASA Astrophysics Data System (ADS)

    Nishino, Hitoshi; Rajpoot, Subhash

    2017-09-01

    We present a system of a self-dual vector-spinor and a self-dual Yang-Mills (YM) field with local nilpotent fermionic symmetry (but not supersymmetry) in D = 2 + 2 dimensions that embeds self-dual supersymmetric YM theory as a special set of exact solutions. Our system has local nilpotent fermionic symmetry generator NIα satisfying the algebra {NIα ,NJβ } = 0 with the adjoint index I of an arbitrary gauge group. Our original field content in D = 2 + 2 is (AIμ ,ψIμ ,χI), where AIμ is the usual YM gauge field, ψIμ is a Majorana-Weyl vector-spinor gauging NIα, while χI is a Majorana-Weyl spinor compensator field needed for consistency. This system embeds self-dual supersymmetric YM system with the field content (AIμ ,λI-) in D = 2 + 2. As other examples, we consider similar systems in D = 7 + 0 and D = 8 + 0 embedding respectively N = 1 / 8 + 7 / 8 and N = (1 / 8 , 1) supersymmetric YM theories with generalized self-dualities, such as FIμν = (1 / 2)fρσμνFIρσ with a generalized octonionic structure constant fρσμν. This result strongly suggests that our local nilpotent fermionic symmetry is more fundamental than the supersymmetric self-dual Yang-Mills systems that are supposed to generate all supersymmetric integrable models in D < 4.

  19. Non-Abelian Dual Superconductivity in SU(3) Yang-Mills Theory Due to Non-Abelian Magnetic Monopoles

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Kato, Seikou; Shinohara, Toru

    The dual superconductivity is the promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture in the SU(3) Yang-Mills theory, and already presented numerical evidences for the restricted field dominance and the non-Abelian magnetic monopole dominance in the string tension, by applying our new formulation of Yang-Mills theory to a lattice. In this talk, we focus on the non-Abelian dual Meissner effect and the type of dual superconductivity. We find that the measured chromo-electric flux tube between a quark and antiquark pair strongly supports the non-Abelian dual Meissner effect due to non-Abelian magnetic monopoles. Moreover, we give a remarkable result that the type of the resulting dual superconductor is the type I in SU(3) Yang-Mills, rather than the border between the type I and II, in marked contrast to the SU(2) case.

  20. Dual computations of non-Abelian Yang-Mills theories on the lattice

    NASA Astrophysics Data System (ADS)

    Cherrington, J. Wade; Christensen, J. Daniel; Khavkine, Igor

    2007-11-01

    In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-Abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet nontrivial case in which the gauge group is non-Abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-Abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.

  1. Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo

    2015-10-01

    We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02χ =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the θ behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.

  2. Perturbative quantization of Yang-Mills theory with classical double as gauge algebra

    NASA Astrophysics Data System (ADS)

    Ruiz Ruiz, F.

    2016-02-01

    Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.

  3. Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Lugo, Adrián R.; Sturla, Mauricio B.

    2010-04-01

    We carry out a gauge invariant analysis of certain perturbations of D - 2-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in D dimensions, a generalization of that recently found in arXiv:0709.0471 [hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.

  4. Massless and massive three-dimensional super Yang-Mills theory and mini-twistor string theory

    SciTech Connect

    Chiou, D.-W.; Ganor, Ori J.; Hong, Yoon Pyo; Kim, Bom Soo; Mitra, Indrajit

    2005-06-15

    We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D=4, where infinitesimal mass terms correspond to vacuum expectation values of certain superconformal gravity fields.

  5. Non-Abelian localization for supersymmetric Yang-Mills-Chern-Simons theories on a Seifert manifold

    NASA Astrophysics Data System (ADS)

    Ohta, Kazutoshi; Yoshida, Yutaka

    2012-11-01

    We derive non-Abelian localization formulas for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface Σ, by using the cohomological approach introduced by Källén. We find that the partition function and the vacuum expectation value of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find that the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on S1×Σ. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the Aharony-Bergman-Jafferis-Maldacena theory deduced from the localization.

  6. On the restoration of supersymmetry in twisted two-dimensional lattice Yang Mills theory

    NASA Astrophysics Data System (ADS)

    Catterall, Simon

    2007-04-01

    We study a discretization of Script N = 2 super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of twisted fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory.

  7. `Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

    NASA Astrophysics Data System (ADS)

    Raptis, Ioannis

    2007-05-01

    Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free Yang-Mills theories, since from the ADG-theoretic perspective gravity is regarded as another gauge field theory. The powerful algebraico-categorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADG-theoretic conception of a field as a pair ({mathcal{E}},{mathcal{D}}) consisting of a vector sheaf {mathcal{E}} and an algebraic connection {mathcal{D}} acting categorically as a sheaf morphism on {mathcal{E}}'s local sections, to introduce a ‘universal’, because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADG-theoretic vantage, vacuum Einstein gravity and free Yang-Mills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.

  8. Ultraviolet divergences in D=8 N=1 supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Kazakov, D. I.; Vlasenko, D. E.

    2017-07-01

    We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in the D=8 N=1 supersymmetric Yang-Mills theory in the planar limit for ladder-type diagrams. We obtain recurrence relations that allow obtaining the leading and subleading divergences in all loops purely algebraically starting from the one-loop diagrams (for the leading poles) and the two-loop diagrams (for the subleading poles). We sum the leading and subleading divergences over all loops using differential equations that are generalizations of the renormalization group equations to nonrenormalizable theories. We discuss the properties of the obtained solutions and the dependence of the constructed counterterms on the scheme.

  9. Inflationary Dilatonic de Sitter Universe from { N} = 4 Super-Yang Mills Theory Perturbed by Scalars

    NASA Astrophysics Data System (ADS)

    Hurtado, John Quiroga

    In this paper a quantum { N} = 4 super-Yang Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

  10. Energy-momentum tensor on the lattice: Nonperturbative renormalization in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Giusti, Leonardo; Pepe, Michele

    2015-06-01

    We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincaré invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang-Mills theory discretized with the standard Wilson action in the presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0 ≤g02≤1 .

  11. The five-loop beta function of Yang-Mills theory with fermions

    NASA Astrophysics Data System (ADS)

    Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J. A. M.; Vogt, A.

    2017-02-01

    We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard overline{MS} scheme for QCD with n f flavours and for pure SU( N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.

  12. Hedgehog loops and finite-temperature transition in Yang-Mills theory

    SciTech Connect

    Belavin, V. A.; Kozlov, I. E.; Chernodub, M. N.

    2009-02-15

    The dynamics of non-Abelian gauge theory can be described not only in terms of local gauge fields but also in terms of nonlocal gauge-invariant variables known as Wilson loops. In Wilson loop space, specific trajectories (defects) are considered on which Wilson loop operators take values in the center of the underlying gauge group. It is shown that, at finite temperature, the density of static (thermal) defects in the Euclidean formulation of Yang-Mills theory is sensitive to the thermodynamic phase transition: numerical calculations reveal that, in contrast to the gluon-plasma phase, where the defect density is high, the density of static defects is very low in the confining phase.

  13. Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory

    SciTech Connect

    Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro

    2009-09-25

    We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 supersymmetric Yang-Mills theory. It takes the form of a Y system based on the integrability of the dual superstring sigma model on the five-dimensional anti-de Sitter space (AdS{sub 5}xS{sup 5}) background. This Y system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS{sub 4}/three-dimensional conformal field theory duality is also treated in a similar fashion.

  14. Large- N limit of the non-local 2D Yang Mills and generalized Yang Mills theories on a cylinder

    NASA Astrophysics Data System (ADS)

    Saaidi, K.; Khorrami, M.

    2002-04-01

    The large-group behavior of the non-local YM_2's and gYM_2's on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for non-local YM_2's on a cylinder with some special boundary conditions are also obtained.

  15. All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory

    SciTech Connect

    Bern, Z.

    2005-01-03

    We compute the next-to-MHV one-loop n-gluon amplitudes in N = 4 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.

  16. N=2 supersymmetric Yang-Mills theories and Whitham integrable hierarchies

    NASA Astrophysics Data System (ADS)

    Edelstein, José D.; Mas, Javier

    1999-07-01

    We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole instanton expansion of the low-energy effective prepotential; (ii) We interpret the slow times of the hierarchy as additional couplings and promote them to spurion superfields that softly break N=2 supersymmetry down to N=0 through deformations associated to higher Casimir operators of the gauge group; (iii) We show that the Seiberg-Witten-Whitham equations provide a set of non-trivial constraints on the form of the strong coupling expansion in the vicinity of the maximal singularities. We use them to check a proposal that we make for the value of the off-diagonal couplings at those points of the moduli space.

  17. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    NASA Astrophysics Data System (ADS)

    Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.

    2016-10-01

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.

  18. Finite temperature and the Polyakov loop in the covariant variational approach to Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Quandt, Markus; Reinhardt, Hugo

    2017-03-01

    We extend the covariant variational approach for Yang-Mills theory in Landau gauge to non-zero temperatures. Numerical solutions for the thermal propagators are presented and compared to high-precision lattice data. To study the deconfinement phase transition, we adapt the formalism to background gauge and compute the effective action of the Polyakov loop for the colour groups SU(2) and SU(3). Using the zero-temperature propagators as input, all parameters are fixed at T = 0 and we find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with lattice data.

  19. Covariant variational approach to Yang-Mills theory: Effective potential of the Polyakov loop

    NASA Astrophysics Data System (ADS)

    Quandt, M.; Reinhardt, H.

    2016-09-01

    We compute the effective action of the Polyakov loop in S U (2 ) and S U (3 ) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low-order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for S U (2 ) and first order for S U (3 ). The critical temperatures obtained are in reasonable agreement with high-precision lattice data.

  20. = 4 supersymmetric Yang-Mills theories in AdS3

    NASA Astrophysics Data System (ADS)

    Kuzenko, Sergei M.; Tartaglino-Mazzucchelli, Gabriele

    2014-05-01

    For all types of = 4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly = 4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The = 4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only = 2 supersymmetry is manifest. Using the off-shell structure of the = 4 vector multiplets, we provide complete = 4 SYM actions in (2,0) AdS superspace for all types of = 4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting = 2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS 3 and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the = 4 Cotton superfield. Thus our results explain the mysterious structure of = 4 supersymmetric Yang-Mills theories on S 3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.

  1. Feynman rules for superfields in N = 1 and N = 2 supersymmetric Yang-Mills theories on the light cone

    SciTech Connect

    Ketov, S.V.

    1985-11-01

    This paper considers N = 1 supersymmetric Yang-Mills theories in dimensions d = 4 and d = 6 on the light cone. The N = 2 theory in d = 4 is obtained by dimensional reduction. The results are represented in the superfield formulation of Mandelstam. Feynman rules for the superfields are obtained. The well-known fact is confirmed that the n = 2 theory in d = 4 has only single-loop divergences in the gauge considered.

  2. N = 4 super-Yang-Mills in LHC superspace part I: classical and quantum theory

    NASA Astrophysics Data System (ADS)

    Chicherin, Dmitry; Sokatchev, Emery

    2017-02-01

    We present a formulation of the maximally supersymmetric N = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N = 4 stress-tensor supermultiplet.

  3. The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Litsey, Sean Christopher

    We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog

  4. Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

    SciTech Connect

    Cucchieri, A.; Mendes, T.

    2008-11-01

    We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p{sup -2-2{kappa}} with {kappa}{approx_equal}0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

  5. Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

    NASA Astrophysics Data System (ADS)

    Tsukiji, Hidekazu; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T.

    2016-11-01

    We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called the Husimi function fH(A ,E ,t ) for the YM field, which is given by a coarse graining of the Wigner function and non-negative. We calculate the Husimi-Wehrl entropy SHW(t )=-Tr fHlog fH defined as an integral over the phase space, for which two adaptations of the test-particle method are used combined with Monte Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show chaotic behavior in the classical limit. We also make a simplification of the multidimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20% overestimate of the Husimi-Wehrl entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.

  6. Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Cucchieri, A.; Mendes, T.

    2008-11-01

    We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p-2-2κ with κ≈0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007)PRVDAQ0556-282110.1103/PhysRevD.75.116004. We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of São Paulo.

  7. Running couplings in equivariantly gauge-fixed SU(N) Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Golterman, Maarten; Shamir, Yigal

    2006-01-01

    In equivariantly gauge-fixed SU(N) Yang-Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup H⊂SU(N) unfixed. Such theories avoid Neuberger’s nogo theorem if the subgroup H contains at least the Cartan subgroup U(1)N-1, and they are thus nonperturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling gtilde 2=ξg2, where g is the gauge coupling and ξ is the gauge parameter, for a class of subgroups including the cases that H=U(1)N-1 or H=SU(M)×SU(N-M)×U(1). The coupling gtilde represents the strength of the interaction of the gauge degrees of freedom associated with the coset SU(N)/H. We find that gtilde , like g, is asymptotically free. We solve the renormalization-group equations for the running of the couplings g and gtilde , and find that dimensional transmutation takes place also for the coupling gtilde , generating an infrared scale Λ˜ which can be larger than or equal to the scale Λ associated with the gauge coupling g, but not smaller. We speculate on the possible implications of these results.

  8. Smooth gauge strings and /D>=2 lattice Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Dubin, Andrey Yu.

    2000-08-01

    Employing the nonabelian duality transformation [A. Dubin, hep-th/9910264], I derive the gauge string form of certain D≥3 lattice Yang-Mills (YM D) theories in the strong coupling (SC) phase. With the judicious choice of the actions, in D≥3 our construction generalizes the Gross-Taylor stringy reformulation of the continuous YM 2 on a 2d manifold. Using the Eguchi-Kawai model as an example, we develop the algorithm to determine the weights w[ M˜] for connected YM-flux worldsheets M˜ immersed into the 2d skeleton of a D≥3 base-lattice. Owing to the invariance of w[ M˜] under a continuous group of area-preserving worldsheet homeomorphisms, the set of weights {w[ M˜]} can be used to define the theory of the smooth YM-fluxes which unambiguously refers to a particular continuous YM D system. I argue that the latter YM D models (with a finite ultraviolet cut-off) for sufficiently large coupling constant(s) are reproduced, to all orders in 1/N, by the smooth gauge string thus associated. The asserted YM D/ String duality allows to make a concrete prediction for the `bare' string tension σ 0 which implies that (in the large N SC regime) the continuous YM D systems exhibit confinement for D≥2. The resulting pattern is qualitatively consistent (in the extreme D=4 SC limit) with the Witten's proposal motivated by the AdS /CFT correspondence.

  9. Integration of Kaluza-Klein modes in Yang-Mills theories

    SciTech Connect

    Novales-Sanchez, H.; Toscano, J. J.

    2011-10-01

    A five-dimensional pure Yang-Mills theory, with the fifth coordinate compactified on the orbifold S{sup 1}/Z{sub 2} of radius R, leads to a four-dimensional theory which is governed by two types of infinitesimal gauge transformations, namely, the well-known standard gauge transformations (SGT) dictated by the SU{sub 4}(N) group under which the zero Fourier modes A{sub {mu}}{sup (0)a} transform as gauge fields, and a set of nonstandard gauge transformations (NSGT) determining the gauge nature of the Kaluza-Klein (KK) excitations A{sub {mu}}{sup (m)a}. By using a SGT-covariant gauge-fixing procedure for removing the degeneration associated with the NSGT, we integrate out the KK excitations and obtain a low-energy effective Lagrangian expansion involving all of the independent canonical-dimension-six operators that are invariant under the SGT of the SU{sub 4}(N) group and that are constituted by light gauge fields, A{sub {mu}}{sup (0)a}, exclusively. It is shown that this effective Lagrangian is invariant under the SGT, but it depends on the gauge-fixing of the gauge KK excitations. Our result shows explicitly that the one-loop contributions of the KK excitations to light (standard) Green's functions are renormalizable.

  10. Non-Abelian dual superconductivity in SU(3) Yang-Mills theory: Dual Meissner effect and type of the vacuum

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Kato, Seikou; Shinohara, Toru

    2013-03-01

    We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic monopole currents induced around the flux. We conclude that the dual superconductivity of the SU(3) Yang-Mills theory is strictly the type I and that this type of dual superconductivity is reproduced by the restricted field and the non-Abelian magnetic monopole part, in sharp contrast to the SU(2) case: the border of type I and type II.

  11. Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory

    SciTech Connect

    Chernodub, M. N.; Morozov, S. M.

    2006-09-01

    We study the embedded QCD monopoles ('quark monopoles') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial, and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anticorrelated with the density of the Dirac eigenmodes. We observe that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low-temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the stringlike objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core which is, however, empty at the very center of the monopole.

  12. Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Chernodub, M. N.; Morozov, S. M.

    2006-09-01

    We study the embedded QCD monopoles (“quark monopoles”) using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial, and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anticorrelated with the density of the Dirac eigenmodes. We observe that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low-temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the stringlike objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core which is, however, empty at the very center of the monopole.

  13. Gluon mass generation and infrared Abelian dominance in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro

    2006-12-01

    Dual superconductivity is believed to be a promising mechanism for quark confinement. Indeed, that this picture is true has been confirmed in the maximal Abelian (MA) gauge. However, it is not yet confirmed in any other gauge, and the MA gauge explicitly breaks color symmetry. To remedy this defect, we propose to use our compact formulation of a non-linear change of variables (NLCV), called once by the Cho-Faddeev-Niemi (CFN) decomposition, on a lattice. This formulation has succeeded to extract the magnetic monopole with integer-valued magnetic charge in the gauge-invariant way. We present measurements of various correlation functions for the operators constructed from the NLCV in SU(2) Yang-Mills theory. Some of our results reproduce previous results obtained in MA gauge, e.g., DeGrand-Toussaint monopole, infrared Abelian dominance and off-diagonal gluon mass generation. These studies preserve color symmetry, which is sharp contrast to the conventional MA gauge. We argue the gauge fixing independence of these results and the implications for quark confinement

  14. Non-intersecting Brownian walkers and Yang-Mills theory on the sphere

    NASA Astrophysics Data System (ADS)

    Forrester, Peter J.; Majumdar, Satya N.; Schehr, Grégory

    2011-03-01

    We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L(N)˜√{N} in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ("watermelons" with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.

  15. Two-dimensional Script N = (2, 2) super Yang-Mills theory on computer

    NASA Astrophysics Data System (ADS)

    Suzuki, Hiroshi

    2007-09-01

    We carry out preliminary numerical study of Sugino's lattice formulation [1, 2] of the two-dimensional Script N = (2, 2) super Yang-Mills theory (2d Script N = (2, 2) SYM) with the gauge group SU(2). The effect of dynamical fermions is included by re-weighting a quenched ensemble by the pfaffian factor. It appears that the complex phase of the pfaffian due to lattice artifacts and flat directions of the classical potential are not problematic in Monte Carlo simulation. Various one-point supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings up to a = 0.5/g with the fixed physical lattice size L = 4.0/g, where g denotes the gauge coupling constant in two dimensions. WT identities implied by an exact fermionic symmetry of the formulation are confirmed in fair accuracy and, for most of these identities, the quantum effect of dynamical fermions is clearly observed. For WT identities expected only in the continuum limit, the results seem to be consistent with the behavior expected from supersymmetry, although we do not see clear distintion from the quenched simulation. We measure also the expectation values of renormalized gauge-invariant bi-linear operators of scalar fields.

  16. Konishi form factor at three loops in N =4 supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Ahmed, Taushif; Banerjee, Pulak; Dhani, Prasanna K.; Rana, Narayan; Ravindran, V.; Seth, Satyajit

    2017-04-01

    We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in N =4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (D R ¯ ) scheme. We show that it satisfies the KG equation in D R ¯ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of the Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of the Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in N =4 .

  17. Duality-symmetric supersymmetric Yang-Mills theory in three dimensions

    SciTech Connect

    Nishino, Hitoshi; Rajpoot, Subhash

    2010-10-15

    We formulate a duality-symmetric N=1 supersymmetric Yang-Mills theory in three dimensions. Our field content is (A{sub {mu}}{sup I},{lambda}{sup I},{phi}{sup I}), where the index I is for the adjoint representation of an arbitrary gauge group G. Our Hodge duality symmetry is F{sub {mu}{nu}}{sup I}=+{epsilon}{sub {mu}{nu}}{sup {rho}D}{sub {rho}{phi}}{sup I}. Because of this relationship, the presence of two physical fields A{sub {mu}}{sup I} and {phi}{sup I} within the same N=1 supermultiplet poses no problem. We can couple this multiplet to another vector multiplet (C{sub {mu}}{sup I},{chi}{sup I};B{sub {mu}{nu}}{sup I}) with 1+1 physical degrees of freedom modulo dim G. Thanks to peculiar couplings and supersymmetry, the usual problem with an extra vector field in a nontrivial representation does not arise in our system.

  18. Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship

    SciTech Connect

    Ghosh, Sushant G.; Dadhich, Naresh

    2010-08-15

    Exact nonstatic spherically symmetric black-hole solutions of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang ansatz, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of Yang-Mills (YM) gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admits strong curvature shell focusing naked singularities violating cosmic censorship. However, there is significant shrinkage of the initial data space for a naked singularity of the HD-Vaidya collapse due to presence of YM gauge charge. The effect of YM gauge charge on structure and location of the apparent and event horizons is also discussed.

  19. Spatially compact solutions and stabilization in Einstein-Yang-Mills-Higgs theories.

    PubMed

    Forgács, Péter; Reuillon, Sébastien

    2005-08-05

    New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet (doublet) representation are presented. They form continuous families parametrized by alpha = M(W)/M(Pl) [M(W) (M(Pl)) denoting the W boson (the Planck) mass]. The corresponding space-times are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as alpha increases (for the triplet) or decreases (for the doublet).

  20. Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group

    NASA Astrophysics Data System (ADS)

    Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.

    2016-11-01

    We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.

  1. Einstein-Yang-Mills from pure Yang-Mills amplitudes

    NASA Astrophysics Data System (ADS)

    Nandan, Dhritiman; Plefka, Jan; Schlotterer, Oliver; Wen, Congkao

    2016-10-01

    We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our results are valid for external bosons in any number of spacetime dimensions. Moreover, they generalize to the superamplitudes in theories with 16 supercharges.

  2. Generating functional and large N limit of nonlocal 2D generalized Yang-Mills theories (nlgYM 2's)

    NASA Astrophysics Data System (ADS)

    Saaidi, K.; Sajadi, H. M.

    2001-01-01

    Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang Mills theories (nlgYM_2's), which are nonlocal in the auxiliary field. This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free energy of W(φ) =φ^{2k} in nlgYM_2 theories at the strong coupling phase (SCP) regime (A > A_c) for large groups. In the specific φ^4 model, we show that the theory has a third order phase transition.

  3. Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD

    SciTech Connect

    Gubser, Steven S.

    2007-12-15

    Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled N=4 super-Yang-Mills theory have appeared recently. I compare the strength of this effect between N=4 gauge theory and QCD, using the static force between external quarks to normalize the 't Hooft coupling. Comparing N=4 and QCD at fixed energy density then leads to a relaxation time of roughly 2 fm/c for charm quarks moving through a quark-gluon plasma at T=250 MeV. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.

  4. Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories

    NASA Astrophysics Data System (ADS)

    Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.

    2010-06-01

    A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.

  5. Double hairpin diagrams and the planar equivalence of N=1 supersymmetric Yang-Mills theory and one-flavor QCD

    NASA Astrophysics Data System (ADS)

    Keith-Hynes, Patrick

    2006-12-01

    Recent work by Armoni, Shifman, and Veneziano suggests a large-N equivalence between super- symmetric Yang-Mills Theory and one-flavor QCD. One consequence of this "orientifold projec- tion" is that scalar and pseudoscalar mesons in one-flavor QCD should have degenerate mass since they lie within the same Wess-Zumino supermultiplet. We use lattice calculations to investigate the mass shifts caused by "double-hairpin" annihilation diagrams in quenched QCD to test for this degeneracy. Similar quark-antiquark annihilation processes are studied in the 2-dimensional CP´N1µ model with quenched fermions.

  6. Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

    2015-05-01

    The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark

  7. A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice

    NASA Astrophysics Data System (ADS)

    Della Morte, Michele; Giusti, Leonardo

    2011-05-01

    We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z N 3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.

  8. Towards the large N limit of pure Nu = 1 super Yang-Mills theory.

    PubMed

    Maldacena, J; Nuñez, C

    2001-01-22

    We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.

  9. Experimentally verifiable Yang-Mills spin 2 gauge theory of gravity with group U(1) x SU(2)

    NASA Astrophysics Data System (ADS)

    Peng, Huei

    1988-06-01

    A Yang-Mills spin 2 gauge theory of gravity is proposed. Based on both the verification of the helicity 2 property of the SU(2) gauge bosons of the theory and the agreement of the theory with most observational and experimental evidence, it is argued that the theory is truly a gravitational theory. Generation by the 4-momentum P sup mu of a fermion of U(1) x SU(2) internal symmetry group for gravity, but not the transformation group T sup 4 is demonstrated. It is shown that the U(1) x SU(2) group represents the time displacement and rotation in ordinary space. Thereby internal space associated with gravity is identical with Minkowski spacetime, so a gauge potential of gravity carries two spacetime indices. Then it is verified that the SU(2) gravitational boson has helicity 2. This theory predicts experimentally verifiable gravitomagnetic fields 4 times smaller than that of general relativity.

  10. Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories

    NASA Astrophysics Data System (ADS)

    Moshin, Pavel Yu.; Reshetnyak, Alexander A.

    2014-11-01

    We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. introduction of finite BRST-antiBRST transformations, being polynomial in powers of a constant Sp(2)-doublet of Grassmann-odd parameters λa and leaving the quantum action of the Yang-Mills theory invariant to all orders in λa; definition of finite field-dependent BRST-antiBRST transformations, being polynomial in powers of an Sp(2)-doublet of Grassmann-odd functionals λa(ϕ) depending on the classical Yang-Mills fields, the ghost

  11. New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N=4 Supersymmetric Yang-Mills Theory.

    PubMed

    Gürdoğan, Ömer; Kazakov, Vladimir

    2016-11-11

    We introduce a family of new integrable quantum field theories in four dimensions by considering the γ-deformed N=4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the 't Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS/CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N=4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.

  12. New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N =4 Supersymmetric Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Gürdoǧan, Ömer; Kazakov, Vladimir

    2016-11-01

    We introduce a family of new integrable quantum field theories in four dimensions by considering the γ -deformed N =4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS /CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N =4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.

  13. Perturbative tests for a large-N reduced model of {N} = {4} super Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato

    2011-11-01

    We study a non-perturbative formulation of {N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

  14. Perturbative tests for a large-N reduced model of mathcal{N} = {4} super Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato

    2012-02-01

    We study a non-perturbative formulation of mathcal{N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

  15. Magnetic black holes and monopoles in a nonminimal Einstein-Yang-Mills theory with a cosmological constant: Exact solutions

    NASA Astrophysics Data System (ADS)

    Balakin, Alexander B.; Lemos, José P. S.; Zayats, Alexei E.

    2016-04-01

    Alternative theories of gravity and their solutions are of considerable importance since, at some fundamental level, the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters, we find a family of exact solutions of the theory depending on five parameters—two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmological constant Λ . We classify completely the family of solutions with respect to the number and the type of horizons and show that the spacetime solutions can have, at most, four horizons. For particular sets of the parameters, these horizons can become double, triple, and quadruple. For instance, for a positive cosmological constant Λ , there is a critical Λc for which the solution admits a quadruple horizon, evocative of the Λc that appears for a given energy density in both the Einstein static and Eddington-Lemaître dynamical universes. As an example of our classification, we analyze solutions in the Drummond-Hathrell nonminimal theory that describe nonminimal black holes. Another application is with a set of regular black holes previously treated.

  16. Yang-Mills origin of gravitational symmetries.

    PubMed

    Anastasiou, A; Borsten, L; Duff, M J; Hughes, L J; Nagy, S

    2014-12-05

    By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincaré symmetry. As a concrete example, we focus on the new minimal (12+12) off shell version of simple four-dimensional supergravity obtained by tensoring the off shell Yang-Mills multiplets (4+4, N_{L}=1) and (3+0, N_{R}=0).

  17. Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension

    NASA Astrophysics Data System (ADS)

    Heffner, J.; Reinhardt, H.

    2015-04-01

    Yang-Mills theory is studied at finite temperature within the Hamiltonian approach in Coulomb gauge by means of the variational principle using a Gaussian-type Ansatz for the vacuum wave functional. Temperature is introduced by compactifying one spatial dimension. As a consequence the finite-temperature behavior is encoded in the vacuum wave functional calculated on the spatial manifold R2×S1(L ) where L-1 is the temperature. The finite-temperature equations of motion are obtained by minimizing the vacuum energy density to two-loop order. We show analytically that these equations yield the correct zero-temperature limit while at infinite temperature they reduce to the equations of the 2 +1 -dimensional theory in accordance with dimensional reduction. The resulting propagators are compared to those obtained from the grand canonical ensemble where an additional Ansatz for the density matrix is required.

  18. Large-N Limit of Nonlocal 2d Generalized Yang-Mills Theories on Non-Orientable Surface

    NASA Astrophysics Data System (ADS)

    Saaidi, Kh.

    The large-group behavior of the nonlocal two-dimensional generalized Yang-Mills theories (nlgYM2's) on arbitrary closed non-orientable surfaces is investigated. It is shown that all order of ϕ2k model of these theories has third order phase transition only on the projective plane (RP2). Also the phase structure of φ 2 + (γ )/(4)φ 4 model of nlgYM2 is studied and it is found that for γ>0, this model has third order phase transition only on RP2. For γ<0, it has third order phase transition on any closed non-orientable surfaces except RP2 and Klein bottle.

  19. An ambitwistor Yang Mills Lagrangian

    NASA Astrophysics Data System (ADS)

    Mason, L. J.; Skinner, D.

    2006-04-01

    We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory.

  20. Nonminimal Einstein-Yang-Mills-Higgs theory: Associated, color, and color-acoustic metrics for the Wu-Yang monopole model

    NASA Astrophysics Data System (ADS)

    Balakin, A. B.; Dehnen, H.; Zayats, A. E.

    2007-12-01

    We discuss a nonminimal Einstein-Yang-Mills-Higgs model with uniaxial anisotropy in the group space associated with the Higgs field. We apply this theory to the problem of propagation of color and color-acoustic waves in the gravitational background related to the nonminimal regular Wu-Yang monopole.

  1. The Study of the Continuum Limit of the Supersymmetric Ward-Takahashi Identity for N = 1 Super Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Feo, A.

    2004-04-01

    The one-loop corrections to the supersymmetric Ward-Takahashi identity (WTi) are investigated in the off-shell regime in the Wilson formulation of the discretized N = 1 Super Yang-Mills (SYM) theory. The study of the continuum limit as well as the renormalization procedure for the supercurrent are presented.

  2. Black p-branes versus black holes in non-asymptotically flat Einstein-Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Habib Mazharimousavi, S.; Halilsoy, M.

    2016-09-01

    We present a class of non-asymptotically flat (NAF) charged black p-branes (BpB) with p-compact dimensions in higher-dimensional Einstein-Yang-Mills theory. Asymptotically the NAF structure manifests itself as an anti-de sitter spacetime. We determine the total mass/energy enclosed in a thin shell located outside the event horizon. By comparing the entropies of BpB with those of black holes in the same dimensions we derive transition criteria between the two types of black objects. Given certain conditions satisfied, our analysis shows that BpB can be considered excited states of black holes. An event horizon r+ versus charge square Q2 plot for the BpB reveals such a transition where r+ is related to the horizon radius rh of the black hole (BH) both with the common charge Q.

  3. Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.

    PubMed

    Basso, Benjamin; Sever, Amit; Vieira, Pedro

    2013-08-30

    We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.

  4. Lattice study of two-dimensional N=(2,2) super Yang-Mills theory at large N

    SciTech Connect

    Hanada, Masanori; Kanamori, Issaku

    2009-09-15

    We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte Carlo simulation for N=2,3,4,5 and then extrapolate the result to N={infinity}. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z{sub N}){sup 2} symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.

  5. Color-Kinematics Duality and Sudakov Form Factor at Five Loops for N =4 Supersymmetric Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Yang, Gang

    2016-12-01

    Using color-kinematics duality, we construct for the first time the full integrand of the five-loop Sudakov form factor in N =4 super-Yang-Mills theory, including nonplanar contributions. This result also provides a first manifestation of the color-kinematics duality at five loops. The integrand is explicitly ultraviolet finite when D <26 /5 , coincident with the known finiteness bound for amplitudes. If the double-copy method could be applied to the form factor, this would indicate an interesting ultraviolet finiteness bound for N =8 supergravity at five loops. The result is also expected to provide an essential input for computing the five-loop nonplanar cusp anomalous dimension.

  6. The Yang-Mills Mass Gap Solution

    NASA Astrophysics Data System (ADS)

    Yablon, Jay R.

    2014-03-01

    The Yang-Mills Mass Gap problem is solved by deriving SU(3)C Chromodynamics as a corollary theory from Yang-Mills gauge theory. The mass gap is filled from finite non-zero eigenvalues of a configuration space inverse perturbation tensor containing vacuum excitations. This results from carefully developing six equivalent views of Yang-Mills gauge theory as having: 1) non-commuting (non-Abelian) gauge fields; 2) gauge fields with non-linear self-interactions; 3) a ``steroidal'' minimal coupling; 4) perturbations; 5) curvature in the gauge space of connections; and 6) gauge fields related to source currents through an infinite recursive nesting. Based on combining classical Yang-Mills electric and magnetic source field equations into a single equation, confinement results from showing how magnetic monopoles of Yang-Mills gauge theory exhibit color confinement and meson flow and have all the color symmetries of baryons, from which we conclude that they are one and the same as baryons. Chiral symmetry breaking results from the recursive behavior of these monopoles coupled with viewing Dirac's gamma matrices as Hamiltonian quaternions extended into spacetime. Finally, with aid from the ``steroidal'' view, the recursive view of Yang-Mills enables polynomial gauge field terms in the Yang-Mills action to be stripped out and replaced by polynomial source current terms prior to path integration. This enables an exact analytical calculation of a non-linear path integral using a closed recursive kernel and yields a non-linear quantum amplitude also with a closed recursive kernel, thus proving the existence of a non-trivial relativistic quantum Yang-Mills field theory on R4 for any simple gauge group G.

  7. Direct evaluation of n-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY formalism

    NASA Astrophysics Data System (ADS)

    Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi

    2016-09-01

    In this paper we extend our techniques, developed in a previous paper [1] for direct evaluation of arbitrary n-point tree-level MHV amplitudes in 4d Yang-Mills and gravity theory using the Cachazo-He-Yuan (CHY) formalism, to the 4d Einstein-Yang-Mills (EYM) theory. Any single-trace color-ordered n-point tree-level MHV amplitude in EYM theory, obtained by a direct evaluation of the CHY formula, is of an elegant factorized form of a Parke-Taylor factor and a Hodges determinant, much simpler and more compact than the existing formulas in the literature. We prove that our new expression is equivalent to the conjectured Selivanov-Bern-De Freitas-Wong (SBDW) formula, with the help of a new theorem showing that the SBDW generating function has a graph theory interpretation. Together with ref. [1], we provide strong analytic evidence for hidden simplicity in quantum field theory.

  8. Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Kamata, Norihiko; Sasaki, Shoichi

    2017-03-01

    We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [J. High Energy Phys. 09 (2014) 018., 10.1007/JHEP09(2014)018]. The tree-level O (a2) improvement can be achieved in a simple manner, where an appropriate weighted average is computed between the plaquette and clover-leaf definitions of the action density ⟨E (t )⟩ measured at every flow time t . We further develop the idea of achieving the tree-level O (a4) improvement within a usage of actions consisting of the 1 ×1 plaquette and 1 ×2 planar loop for both the flow and gauge actions. For testing our proposal, we present numerical results for ⟨E (t )⟩ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings (a ≈0.1 ,0.07 , and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on t2⟨E (t )⟩ in the relatively small-t regime for up to t ≳a2 . To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the ΛMS ¯ parameter and the new reference scale tX, which is defined through tX2⟨E (tX)⟩=X for the smaller X , e.g., X =0.15 . It is found that √{t0.15 }ΛMS ¯ shows a nearly perfect scaling behavior as a function of a2 regardless of the types of gauge action and flow, after tree-level improvement is achieved up to O (a4) . Further detailed study of the scaling behavior exposes the presence of the remnant O (g2 na2) corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all O (a2) effects, we show that the O (g2 na2) corrections can be well under control even by the simplest tree-level O (a2) improved flow.

  9. Supergravity duals to the noncommutative N=4 super Yang-Mills theory in the infinite momentum frame

    NASA Astrophysics Data System (ADS)

    Kim, Hongsu

    2003-09-01

    In this work, the construction of supergravity duals to the noncommutative N=4 super Yang-Mills theory in the infinite momentum frame but with a constant momentum density is attempted. In the absence of noncommutativity, it has been known for some time that the previous AdS5/CFT4 correspondence should be replaced by the K5/CFT4 correspondence (with K(p+2) denoting the generalized Kaigorodov spacetime) with a pp wave propagating on the Bogomol’nyi-Prasad-Sommerfield brane worldvolume. Interestingly enough, putting together the two additions, i.e., the introduction of noncommutativity and at the same time that of the pp wave along the brane worldvolume, leads to quite nontrivial consequences such as the emergence of “time-space” noncommutativity in addition to the “space-space” noncommutativity in the manifold on which the dual gauge theory is defined. Taking the gravity decoupling limit, it has been realized that, for small u, the solutions all reduce to K5×S5 geometry, confirming our expectation that the IR dynamics of the dual gauge theory should be unaffected by the noncommutativity while, as u→∞, the solutions start to deviate significantly from the K5×S5 limit, indicating that the UV dynamics of dual gauge theory is heavily distorted by the effect of noncommutativity.

  10. Faddeev-Popov-ghost propagators for Yang-Mills theories and perturbative quantum gravity in the covariant gauge in de Sitter spacetime

    SciTech Connect

    Faizal, Mir; Higuchi, Atsushi

    2008-09-15

    The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore, we propose that the IR-divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to using the effective FP-ghost propagators, which we present in an explicit form, obtained by removing the modes responsible for the IR divergences. We also make some comments on the corresponding propagators in anti-de Sitter spacetime.

  11. Distinctive ultraviolet structure of extra-dimensional Yang-Mills theories by integration of heavy Kaluza-Klein modes

    NASA Astrophysics Data System (ADS)

    García-Jiménez, I.; Novales-Sánchez, H.; Toscano, J. J.

    2016-05-01

    One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, n , of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge-independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension k are finite as long as k >4 +n . Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable.

  12. Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Guimaraes, M. S.; Pereira, A. D.; Sorella, S. P.

    2016-12-01

    In this paper, we discuss nonperturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than 4 in the Landau gauge and within the refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the refined Gribov-Zwanziger action from five to four dimensions, a nonperturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism [1 M. A. L. Capri, M. S. Guimaraes, I. F. Justo, L. F. Palhares, and S. P. Sorella, Phys. Rev. D 90, 085010 (2014)., 10.1103/PhysRevD.90.085010] to generalize the refined Gribov-Zwanziger construction to the matter sector.

  13. Representations of Super Yang-Mills Algebras

    NASA Astrophysics Data System (ADS)

    Herscovich, Estanislao

    2013-06-01

    We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.

  14. The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

    SciTech Connect

    Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.

    2006-11-15

    We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.

  15. Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

    NASA Astrophysics Data System (ADS)

    Gußmann, Alexander

    2017-03-01

    The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

  16. Yang Mills Chern Simons supergravity

    NASA Astrophysics Data System (ADS)

    Lü, H.; Pope, C. N.; Sezgin, E.

    2004-06-01

    N = (1, 0) supergravity in six dimensions admits AdS3 × S3 as a vacuum solution. We extend our recent results presented in Lü et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang Mills Chern Simons supergravity in D = 3, up to quartic fermion terms, by S3 group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang Mills kinetic terms as well as topological Chern Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.

  17. Yang-Mills mass gap at large-N, noncommutative YM theory, topological quantum field theory and hyperfiniteness

    NASA Astrophysics Data System (ADS)

    Bochicchio, Marco

    2015-03-01

    We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse-Smale-Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang-Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in (1)/(N), a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a

  18. An Energy Gap for Complex Yang-Mills Equations

    NASA Astrophysics Data System (ADS)

    Huang, Teng

    2017-08-01

    We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory Appl. 11 (2012), 185-198], when Riemannian manifold X of dimension n≥ 2 satisfies certain conditions.

  19. Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

    SciTech Connect

    Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study

    2012-02-15

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.

  20. Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory

    NASA Astrophysics Data System (ADS)

    Wali, Kameshwar; Viet, Nguyen Ali

    2017-01-01

    A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluza-Klein theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the coupling of the chiral spinors in the generalized gravity together with some new interactions. In particular, the currently prevailing gravity-QCD quark and gravity-electroweak-quark and lepton models are shown to follow as special cases of the general framework.

  1. 2D Kac-Moody symmetry of 4D Yang-Mills theory

    SciTech Connect

    He, Temple; Mitra, Prahar; Strominger, Andrew

    2016-10-25

    Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.

  2. 2D Kac-Moody symmetry of 4D Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    He, Temple; Mitra, Prahar; Strominger, Andrew

    2016-10-01

    Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G -Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.

  3. Regularization of two-dimensional supersymmetric Yang-Mills theory via non-commutative geometry

    NASA Astrophysics Data System (ADS)

    Valavane, K.

    2000-11-01

    The non-commutative geometry is a possible framework to regularize quantum field theory in a non-perturbative way. This idea is an extension of the lattice approximation by non-commutativity that allows us to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on a supersphere. This paper is a generalization of this latter work to more general gauge groups.

  4. Abelian Yang-Mills Theory on Real Tori and Theta Divisors of Klein Surfaces

    NASA Astrophysics Data System (ADS)

    Okonek, Christian; Teleman, Andrei

    2013-11-01

    The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.

  5. Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.

    2017-05-01

    The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.

  6. θ dependence in S U (3 ) Yang-Mills theory from analytic continuation

    NASA Astrophysics Data System (ADS)

    Bonati, Claudio; D'Elia, Massimo; Scapellato, Aurora

    2016-01-01

    We investigate the topological properties of the S U (3 ) pure gauge theory by performing numerical simulations at imaginary values of the θ parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of θ and exploiting analytic continuation, we determine the free energy density up to the sixth order in θ , f (θ ,T )=f (0 ,T )+1/2 χ (T )θ2(1 +b2(T )θ2+b4(T )θ4+O (θ6)) . That permits us to achieve determinations with improved accuracy, in particular for the higher-order terms, with control over the continuum and the infinite-volume extrapolations. We obtain b2=-0.0216 (15 ) and |b4|≲4 ×10-4 .

  7. Towards the Exact Dilatation Operator of {N} = 4 Super Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Ryzhov, Anton V.

    I present a summary of hep-th/0404215, which suggested a novel way of organizing the dilatation operator D of planar {N} = 4 SYM in the SU(2) sector. Instead of the usual perturbative expansion in powers of λ, we split D into parts D(n) according to the number n of independent pairwise interactions between spins at different sites. The BMN limit fixes D(1) completely, and it has regular expansions at both small and large values of λ. Anomalous dimensions of "long" operators in the two-scalar sector then generically scale as √λ at large λ, i.e. in the same way as energies of semiclassical states in the dual AdS5 ×S5 string theory.

  8. Generalized gaugino condensation in super Yang-Mills theories: Discrete R symmetries and vacua

    NASA Astrophysics Data System (ADS)

    Kehayias, John

    2010-12-01

    One can define generalized models of gaugino condensation as theories that dynamically break a discrete R symmetry but do not break supersymmetry. We consider general examples consisting of gauge and matter fields and the minimal number of gauge-singlet fields to avoid flat directions in the potential. We explore which R symmetries can arise and their spontaneous breaking. In general, we find that the discrete symmetry is Z2b0R, and the number of supersymmetric vacua is b0, where b0 is the coefficient of the one-loop beta function. Results are presented for various groups, including SU(Nc), SO(Nc), Sp(2Nc), and G2, for various numbers of flavors, Nf, by several methods. This analysis can also apply to the other exceptional groups and, thus, all simple Lie groups. We also comment on model-building applications where a discrete R symmetry, broken by the singlet vacuum expectation values, can account for μ-type terms and allow a realistic Higgs spectrum naturally.

  9. Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Nakagawa, Y.; Voigt, A.; Ilgenfritz, E.-M.; Müller-Preussker, M.; Nakamura, A.; Saito, T.; Sternbeck, A.; Toki, H.

    2009-06-01

    We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb-gauge theory carrying out a joint analysis of data collected independently at the Research Center for Nuclear Physics, Osaka and Humboldt University, Berlin. We focus on the scaling behavior of these propagators at β=5.8,…,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at a large momentum. As a byproduct we obtain the respective lattice scale dependences a(β) for the transversal gluon and the ghost propagator which indeed run faster with β than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(β) dependence as determined from the instantaneous time-time gluon propagator, D44, remains a problem, though. The role of residual gauge-fixing influencing D44 is discussed.

  10. Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

    NASA Astrophysics Data System (ADS)

    Dudal, D.; Sobreiro, R. F.; Sorella, S. P.; Verschelde, H.

    2005-07-01

    The local composite operator A2μ is added to the Zwanziger action, which implements the restriction to the Gribov region Ω in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger’s action with the inclusion of the operator A2μ is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows us to study the dimension two gluon condensate by the local composite operator formalism when the restriction to the Gribov region Ω is taken into account. The resulting effective action is evaluated at one-loop order in the MS¯ scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate , are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator A2μ, the resulting vacuum energy is always positive at one-loop order, independently from the choice of the renormalization scheme and scale. In the presence of , we are unable to come to a definite conclusion at the order considered. In the MS¯ scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behavior of the gluon and ghost propagators, we recover the well-known consequences of the restriction to the Gribov region, and this in the presence of , i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behavior is in qualitative agreement with the results obtained from the studies of the

  11. Infinite dimensional symmetries of self-dual Yang-Mills

    NASA Astrophysics Data System (ADS)

    Mansfield, Paul; Wardlow, Adam

    2009-08-01

    We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra in the group algebra of isometries.

  12. Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N =4 Supersymmetric Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet

    2016-05-01

    We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.

  13. Gauge-independent "Abelian" and magnetic-monopole dominance, and the dual Meissner effect in lattice S U (2 ) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Kato, Seikou; Kondo, Kei-Ichi; Shibata, Akihiro

    2015-02-01

    In the S U (2 ) Yang-Mills theory on the four-dimensional Euclidean lattice, we confirm the gauge-independent "Abelian" dominance (or the restricted field dominance) and gauge-independent magnetic-monopole dominance in the string tension of the linear potential extracted from the Wilson loop in the fundamental representation. The dual Meissner effect is observed by demonstrating the squeezing of the chromoelectric field flux connecting a pair of a quark and an antiquark. In addition, the circular magnetic-monopole current is induced around the chromoelectric flux. The type of the dual superconductivity is also determined by fitting the result with the dual Ginzburg-Landau model. Thus, the dual superconductor picture for quark confinement is supported in a gauge-independent manner. These results are obtained based on a reformulation of the lattice Yang-Mills theory based on the change of variables à la Cho-Duan-Ge-Faddeev-Niemi combined with a non-Abelian Stokes theorem for the Wilson loop operator. We give a new procedure (called the reduction) for obtaining the color direction field that plays the central role in this reformulation.

  14. Yang-Mills for Historians and Philosophers

    NASA Astrophysics Data System (ADS)

    Crease, R. P.

    The phrase "Yang-Mills" can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the "Pauli snag," or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.

  15. Analytic representations of Yang-Mills amplitudes

    NASA Astrophysics Data System (ADS)

    Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.; Feng, Bo

    2016-12-01

    Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space-fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.

  16. Supersymmetric electric-magnetic duality in D =3 +3 and D =5 +5 dimensions as foundation of self-dual supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Nishino, Hitoshi; Rajpoot, Subhash

    2016-05-01

    We present electric-magnetic (EM)-duality formulations for non-Abelian gauge groups with N =1 supersymmetry in D =3 +3 and 5 +5 space-time dimensions. We show that these systems generate self-dual N =1 supersymmetric Yang-Mills (SDSYM) theory in D =2 +2 . For a N =2 supersymmetric EM-dual system in D =3 +3 , we have the Yang-Mills multiplet (Aμ I,λA I) and a Hodge-dual multiplet (Bμν ρ I,χA I) , with an auxiliary tensors Cμν ρ σ I and Kμ ν. Here, I is the adjoint index, while A is for the doublet of S p (1 ). The EM-duality conditions are Fμν I=(1 /4 !)ɛμν ρ σ τ λGρσ τ λ I with its superpartner duality condition λA I=-χA I . Upon appropriate dimensional reduction, this system generates SDSYM in D =2 +2 . This system is further generalized to D =5 +5 with the EM-duality condition Fμν I=(1 /8 !)ɛμν ρ1⋯ρ8Gρ1⋯ρ8 I with its superpartner condition λI=-χI . Upon appropriate dimensional reduction, this theory also generates SDSYM in D =2 +2 . As long as we maintain Lorentz covariance, D =5 +5 dimensions seems to be the maximal space-time dimensions that generate SDSYM in D =2 +2 . Namely, EM-dual system in D =5 +5 serves as the Master Theory of all supersymmetric integrable models in dimensions 1 ≤D ≤3 .

  17. On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

    NASA Astrophysics Data System (ADS)

    Baxter, J. Erik; Winstanley, Elizabeth

    2016-02-01

    We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

  18. On the global existence of hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

    NASA Astrophysics Data System (ADS)

    Baxter, J. Erik

    2016-10-01

    We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called regular case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS {mathfrak {su}}(N) system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for Λ <0, solutions are much less constrained as r→ infty , making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of |Λ |→ infty . In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the {mathfrak {su}}(N) case proved important to stability.

  19. On the existence of soliton and hairy black hole solutions of {\\mathfrak {su}}(N) Einstein Yang Mills theory with a negative cosmological constant

    NASA Astrophysics Data System (ADS)

    Baxter, J. E.; Winstanley, Elizabeth

    2008-12-01

    We study the existence of soliton and black hole solutions of four-dimensional {\\mathfrak {su}}(N) Einstein Yang Mills theory with a negative cosmological constant. We prove the existence of non-trivial solutions for any integer N, with N - 1 gauge field degrees of freedom. In particular, we prove the existence of solutions in which all the gauge field functions have no zeros. For fixed values of the parameters (at the origin or event horizon, as applicable) defining the soliton or black hole solutions, if the magnitude of the cosmological constant is sufficiently large, then the gauge field functions all have no zeros. These latter solutions are of special interest because at least some of them will be linearly stable.

  20. Existence of topological hairy dyons and dyonic black holes in anti-de Sitter su(N) Einstein-Yang-Mills theory

    SciTech Connect

    Baxter, J. Erik

    2016-02-15

    We investigate dyonic black hole and dyon solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer N, with 2N − 2 gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our main result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeros, which is likely important to the stability of the solutions.

  1. Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime

    NASA Astrophysics Data System (ADS)

    Shepherd, Ben L.; Winstanley, Elizabeth

    2016-03-01

    We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

  2. Massive loops in thermal SU(2) Yang-Mills theory: Radiative corrections to the pressure beyond two loops

    NASA Astrophysics Data System (ADS)

    Bischer, Ingolf; Grandou, Thierry; Hofmann, Ralf

    2017-07-01

    We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang-Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

  3. YANG-MILLS FIELDS AND THE LATTICE.

    SciTech Connect

    CREUTZ,M.

    2004-05-18

    The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.

  4. Study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon

    NASA Astrophysics Data System (ADS)

    Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.

    2006-11-01

    We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger’s treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, ZgZA1/2=1, relating the renormalization factors of the gauge coupling constant Zg and of the diagonal gluon field ZA, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.

  5. A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges

    NASA Astrophysics Data System (ADS)

    Capri, M. A. L.; Fiorentini, D.; Pereira, A. D.; Sorella, S. P.

    2017-08-01

    In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.

  6. The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \\mathcal{N} $ = 4 super-Yang-Mills theory

    SciTech Connect

    None, None

    2014-06-19

    We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar NN = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N3LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.

  7. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    NASA Astrophysics Data System (ADS)

    Chankowski, Piotr H.; Lewandowski, Adrian; Meissner, Krzysztof A.

    2016-11-01

    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional overline{MS} scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the overline{MS} scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  8. Landau gauge Yang-Mills correlation functions

    NASA Astrophysics Data System (ADS)

    Cyrol, Anton K.; Fister, Leonard; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils

    2016-09-01

    We investigate Landau gauge S U (3 ) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalization group. Particular focus is put on the dynamical creation of the gluon mass gap at nonperturbative momenta and the consistent treatment of quadratic divergences. The nonperturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as the only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

  9. Einstein Manifolds as Yang-Mills Instantons

    NASA Astrophysics Data System (ADS)

    Oh, John J.; Yang, Hyun Seok

    2013-07-01

    It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)L × SU(2)R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)L instantons and SU(2)R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)L and anti-instantons in SU(2)R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.

  10. Stationary axisymmetric SU(2) Einstein-Yang-Mills fields with restricted circularity conditions are Abelian

    NASA Astrophysics Data System (ADS)

    Chinea, F. J.; Navarro-Lérida, F.

    2002-03-01

    In this paper we prove that in a stationary axisymmetric SU(2) Einstein-Yang-Mills theory the most reasonable circularity conditions that can be considered for the Yang-Mills fields imply in fact that the field is of embedded Abelian type, or else that the metric is not asymptotically flat.

  11. Quantum Yang-Mills Dark Energy

    NASA Astrophysics Data System (ADS)

    Pasechnik, Roman

    2016-02-01

    In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann--Lema\\'itre--Robertson--Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state.

  12. Spontaneously broken Yang-Mills-Einstein supergravities as double copies

    NASA Astrophysics Data System (ADS)

    Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu

    2017-06-01

    Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicit examples with N=2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy fields and parameters. We also briefly discuss the application of our results to N=4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.

  13. Non-Abelian strings in supersymmetric Yang-Mills

    SciTech Connect

    Shifman, M.

    2012-09-26

    I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.

  14. Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST-invariant two-point correlation function

    NASA Astrophysics Data System (ADS)

    Capri, M. A. L.; Dudal, D.; Pereira, A. D.; Fiorentini, D.; Guimaraes, M. S.; Mintz, B. W.; Palhares, L. F.; Sorella, S. P.

    2017-02-01

    In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations Ah . Such configurations can be obtained through the minimization of the functional Amin2 along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of ⟨Aμh(k )Aνh(-k )⟩ are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter α entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator ⟨Aμh(k )Aνh(-k )⟩ enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of ⟨Aμh(k )Aνh(-k )⟩ as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use ⟨Aμh(k )Aνh(-k )⟩ to probe the pole structure of the massive gauge boson in a gauge-invariant fashion.

  15. Spontaneously broken Yang-Mills-Einstein supergravities as double copies

    DOE PAGES

    Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

    2017-06-13

    Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this article we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs elds. One gaugetheory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicitmore » examples with N = 2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy elds and parameters. We also briefly discuss the application of our results to N = 4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.« less

  16. Yang-Mills for historians and philosophers

    NASA Astrophysics Data System (ADS)

    Crease, R. P.

    2016-01-01

    The phrase “Yang-Mills” can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the “Pauli snag,” or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.

  17. Yang-Mills instanton sheaves

    NASA Astrophysics Data System (ADS)

    Lai, Sheng-Hong; Lee, Jen-Chi; Tsai, I.-Hsun

    2017-02-01

    The SL(2 , C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP3 similar to the case of SU(2) ADHM construction, the SL(2 , C) instanton solutions can be used to explicitly construct instanton sheaves on CP3. Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2 , C) instantons on S4 which do not exist for SU(2) instantons.

  18. N=(0,2) deformation of the CP(1) model: Two-dimensional analog of N=1 Yang-Mills theory in four dimensions

    NASA Astrophysics Data System (ADS)

    Cui, Xiaoyi; Shifman, M.

    2012-02-01

    We consider two-dimensional N=(0,2) sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, Nf right-handed fermions. Our task is to derive expressions for the β functions valid to all orders. To this end we use a variety of methods: (i) perturbative analysis; (ii) instanton calculus; (iii) analysis of the supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, and some other arguments. All these arguments, combined, indicate a direct parallel between the heterotic N=(0,2) CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the minimal N=(0,2) CP(1) model is similar to N=1 supersymmetric gluodynamics. Its exact β function can be found; it has the structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β function of supersymmetric gluodynamics. The passage to nonminimal N=(0,2) sigma models is equivalent to adding matter. In this case an NSVZ-type exact relation between the β function and the anomalous dimensions γ of the “matter” fields is established. We derive an analog of the Konishi anomaly. At large Nf our β function develops an infrared fixed point at small values of the coupling constant (analogous to the Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal window. At Nf=1 the model under consideration reduces to the well-known N=(2,2) CP(1) model.

  19. Black-hole black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang Mills theory on a circle

    NASA Astrophysics Data System (ADS)

    Aharony, Ofer; Marsano, Joseph; Minwalla, Shiraz; Wiseman, Toby

    2004-11-01

    We review and extend earlier work that uses the AdS/CFT correspondence to relate the black-hole black-string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric (1 + 1)-dimensional SU(N) gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, the (1 + 1)-dimensional theory reduces to a (0 + 1)-dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole black string-like phase transition in the large N limit. We demonstrate that a simple Landau Ginzburg-like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first-order and a second-order transition.

  20. Exotic polarizations of D2 branes and oblique vacua of (2+1)-dimensional super Yang-Mills theory

    SciTech Connect

    Bena, Iosif; Nudelman, Aleksey

    2000-12-15

    We investigate the oblique vacua in the perturbed (2+1)-dimensional gauge theory living on D2-branes. The string theory dual of these vacua is expected to correspond to polarizations of the D2-branes into NS5-branes with D4-brane charge. We perturb the gauge theory by adding fermion masses. In the nonsupersymmetric case, we also consider the effect of slight variations of the masses of the scalars. For certain ranges of scalar masses we find oblique vacua. We show that D4 charge is an essential ingredient in understanding D2 {yields} NS5 polarizations. We find that some of the polarization states which appear as metastable vacua when the D4 charge is not considered are in fact unstable. They decay by acquiring a D4 charge, tilting and shrinking to zero size.

  1. Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

    NASA Astrophysics Data System (ADS)

    Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu

    2017-07-01

    Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.

  2. No-go for partially massless spin-2 Yang-Mills

    DOE PAGES

    Garcia-Saenz, Sebastian; Hinterbichler, Kurt; Joyce, Austin; ...

    2016-02-05

    There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. In this paper, we give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.

  3. Expansion of Einstein-Yang-Mills amplitude

    NASA Astrophysics Data System (ADS)

    Fu, Chih-Hao; Du, Yi-Jian; Huang, Rijun; Feng, Bo

    2017-09-01

    In this paper, we study from various perspectives the expansion of tree level single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes. By applying the gauge invariance principle, a programable recursive construction is devised to expand EYM amplitude with arbitrary number of gravitons into EYM amplitudes with fewer gravitons. Based on this recursive technique we write down the complete expansion of any single trace EYM amplitude in the basis of color-order Yang-Mills amplitude. As a byproduct, an algorithm for constructing a polynomial form of the BCJ numerator for Yang-Mills amplitudes is also outlined in this paper. In addition, by applying BCFW recursion relation we show how to arrive at the same EYM amplitude expansion from the on-shell perspective. And we examine the EYM expansion using KLT relations and show how to evaluate the expansion coefficients efficiently.

  4. Yang-Mills glueballs as closed bosonic strings

    NASA Astrophysics Data System (ADS)

    Dubovsky, Sergei; Hernández-Chifflet, Guzmán

    2017-02-01

    We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang-Mills theory both in D = 3 and D = 4 space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, P-and C-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately 12 + 22 + 32 + 52 = 39 lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice data for long strings.

  5. An exploratory study of Yang-Mills three-point functions at non-zero temperature

    NASA Astrophysics Data System (ADS)

    Huber, Markus Q.

    2017-03-01

    Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.

  6. HYM-flation: Yang-Mills cosmology with Horndeski coupling

    NASA Astrophysics Data System (ADS)

    Davydov, E.; Gal'tsov, D.

    2016-02-01

    We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

  7. Dirac equations for generalised Yang-Mills systems

    NASA Astrophysics Data System (ADS)

    Lechtenfeld, O.; Nahm, W.; Tchrakian, D. H.

    1985-11-01

    We present Dirac equations in 4 p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a “BPST” background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results.

  8. Yang-Mills generalization of the geometrical collective model

    NASA Astrophysics Data System (ADS)

    Rosensteel, George; Sparks, Nick

    2015-04-01

    The geometrical or Bohr-Mottelson model is generalized and recast as a Yang-Mills theory. The gauge symmetry determines conservation of Kelvin circulation. The circulation commutes with the Hamiltonian when it is the sum of the kinetic energy and a potential that depends only on deformation. The conventional Bohr-Mottelson model is the special case of circulation zero, and wave functions are complex-valued. In the generalization, any quantized value of the circulation is allowed, and the wave functions are vector-valued. The Yang-Mills formulation introduces a new coupling between the geometrical and intrinsic degrees of freedom. The coupling appears in the covariant derivative term of the collective kinetic energy. This kind of coupling is sometimes called ``magnetic'' because of the analogy with electrodynamics.

  9. Comments on twisted indices in 3d supersymmetric gauge theories

    NASA Astrophysics Data System (ADS)

    Closset, Cyril; Kim, Heeyeon

    2016-08-01

    We study three-dimensional {N} = 2 supersymmetric gauge theories on Σ g × S 1 with a topological twist along Σ g , a genus- g Riemann surface. The twisted supersymmetric index at genus g and the correlation functions of half-BPS loop operators on S 1 can be computed exactly by supersymmetric localization. For g = 1, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe equations for the theory on {{R}}^2× {S}^1 . This also provides a powerful and simple tool to study 3d {N} = 2 Seiberg dualities. Finally, we study A- and B-twisted indices for {N} = 4 supersymmetric gauge theories, which turns out to be very useful for quantitative studies of three-dimensional mirror symmetry. We also briefly comment on a relation between the S 2 × S 1 twisted indices and the Hilbert series of {N} = 4 moduli spaces.

  10. Degenerate, strong and stable Yang-Mills-Higgs pairs

    NASA Astrophysics Data System (ADS)

    Hu, Zhi; Huang, Pengfei

    2017-10-01

    In this paper, we introduce some notions on the Hitchin pair consisting of a Chern connection and a Higgs field closely related to the first and second variations of Yang-Mills-Higgs functional, such as degenerate Hitchin pair, (strong) Yang-Mills-Higgs pair, and stable Yang-Mills-Higgs pair. We investigate some properties of such pairs under the various contexts.

  11. Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence

    NASA Astrophysics Data System (ADS)

    Luo, Yuan; Tan, Meng-Chwan; Yagi, Junya; Zhao, Qin

    2015-02-01

    We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface Σ and a three-manifold M, and show that when Σ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on M. Based on these results, we establish a correspondence between three-dimensional = 2 superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.

  12. Fate of Yang-Mills black hole in early Universe

    SciTech Connect

    Nakonieczny, Lukasz; Rogatko, Marek

    2013-02-21

    According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.

  13. Yang-Mills effective action at high temperature

    NASA Astrophysics Data System (ADS)

    Oswald, M.

    2005-06-01

    Yang-Mills theory undergoes a transition from a confined to a deconfined phase in the intermediate temperature regime, where perturbation theory fails. In order to approach this phase transition from the high temperature side we study the effective action for the eigenvalues of the order parameter, the Polyakov loop, in the whole range of its possible variation. By means of a covariant derivative expansion we integrate out fast varying quantum fluctuations around background gluon fields and assume that these are slowly varying, but that the amplitude of A4 is arbitrary. Our results can be used to study correlation functions of the order parameter at high temperatures.

  14. Fate of Yang-Mills black hole in early Universe

    NASA Astrophysics Data System (ADS)

    Nakonieczny, Łukasz; Rogatko, Marek

    2013-02-01

    According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.

  15. N=2 super Yang-Mills action as a Becchi-Rouet-Stora-Tyutin term, topological Yang-Mills action, and instantons

    NASA Astrophysics Data System (ADS)

    Ülker, K.

    2003-10-01

    By constructing a nilpotent extended Becchi-Rouet-Stora-Tyutin (BRST) operator s¯ that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell super Yang-Mills action can be represented as an exact BRST term s¯Ψ, if the gauge fermion Ψ is allowed to depend on the inverse powers of supersymmetry (SUSY) ghosts. By using this nonanalytical structure of the gauge fermion (via inverse powers of supersymmetry ghosts), we give field redefinitions in terms of composite fields of SUSY ghosts and N=2 fields and we show that Witten’s topological Yang-Mills (TYM) theory can be obtained from the ordinary Euclidean N=2 super Yang-Mills (SYM) theory directly by using such field redefinitions. In other words, TYM theory is obtained as a change of variables (without twisting). As a consequence it is found that physical and topological interpretations of N=2 SYM theory are intertwined together due to the requirement of analyticity of global SUSY ghosts. Moreover, after an instanton-inspired truncation of the model is used, we show that the given field redefinitions yield the Baulieu-Singer formulation of topological Yang-Mills theory.

  16. A consistent measure for lattice Yang-Mills

    NASA Astrophysics Data System (ADS)

    Vilela Mendes, R.

    2017-01-01

    The construction of a consistent measure for Yang-Mills is a precondition for an accurate formulation of nonperturbative approaches to QCD, both analytical and numerical. Using projective limits as subsets of Cartesian products of homomorphisms from a lattice to the structure group, a consistent interaction measure and an infinite-dimensional calculus have been constructed for a theory of non-Abelian generalized connections on a hypercubic lattice. Here, after reviewing and clarifying past work, new results are obtained for the mass gap when the structure group is compact.

  17. Yang-Mills correlators across the deconfinement phase transition

    NASA Astrophysics Data System (ADS)

    Reinosa, U.; Serreau, J.; Tissier, M.; Tresmontant, A.

    2017-02-01

    We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.

  18. A walk through superstring theory with an application to Yang-Mills theory: K-strings and D-branes as gauge/gravity dual objects

    NASA Astrophysics Data System (ADS)

    Stiffler, Kory M.

    Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dp-branes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k-string is a colorless combination of quark-antiquark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2 + 1 and 3 + 1 space-time dimensions as the energy of D p-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge as the one loop quantum corrections to the Dp-brane energy. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.

  19. Gauge-covariant decomposition and magnetic monopole for G (2 ) Yang-Mills field

    NASA Astrophysics Data System (ADS)

    Matsudo, Ryutaro; Kondo, Kei-Ichi

    2016-08-01

    We provide a gauge-covariant decomposition of the Yang-Mills field with the exceptional gauge group G (2 ), which extends the field decomposition proposed by Cho, Duan-Ge, and Faddeev-Niemi for the S U (N ) Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of G (2 ). The resulting new form is used to define gauge-invariant magnetic monopoles in the G (2 ) Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semisimple Lie group other than S U (N ) and G (2 ).

  20. Orbifold singularities, Lie algebras of the third kind (LATKes), and pure Yang-Mills with matter

    SciTech Connect

    Friedmann, Tamar

    2011-02-15

    We discover the unique, simple Lie algebra of the third kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is one-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism. The World in a Point?; Blow-up ofC{sup 3}/Z{sub 3}| Dynkin diagram of the LATKe; {center_dot}; Pure Yang-Mills with matter

  1. Statefinder Diagnostic for the Yang-Mills Dark Energy Model

    NASA Astrophysics Data System (ADS)

    Zhao, Wen

    We study the statefinder parameters in the Yang-Mills condensate dark energy models, and find that the evolving trajectories of these models are different from those of other dark energy models. We also define two eigenfunctions of the Yang-Mills condensate dark energy models. The values of these eigenfunctions are quite close to zero if the equation of state of the Yang-Mills condensate is not far from -1, which can be used to simply differentiate between the Yang-Mills condensate models and other dark energy models.

  2. The Plane-Wave/Super Yang-Mills Duality

    SciTech Connect

    Sadri, D

    2003-10-14

    We present a self-contained review of the Plane-wave/super-Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large R-charge sector of N=4, D=4 superconformal U(N) gauge theory. This duality is a specification of the usual AdS/CFT correspondence in the ''Penrose limit''. The Penrose limit of AdS{sub 5} S{sup 5} leads to the maximally supersymmetric ten dimensional plane-wave (henceforth the plane-wave) and corresponds to restricting to the large R-charge sector, the BMN sector, of the dual superconformal field theory. After assembling the necessary background knowledge, we state the duality and review some of its supporting evidence. We review the suggestion by 't Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. We discuss plane-waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds, then present an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. We then make precise the statement of the proposed duality, classify the BMN operators, and mention some extensions of the proposal. We move on to study the gauge theory side of the duality, studying both quantum and non-planar corrections to correlation functions of BMN operators, and their operator product expansion. The important issue of operator mixing and the resultant need for re-diagonalization is stressed. Finally, we study strings on the plane-wave via light-cone string field theory, and demonstrate agreement on the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.

  3. Conformal properties of the BPST instantons of the generalised Yang-Mills system

    NASA Astrophysics Data System (ADS)

    O'Sé, Diarmuid; Tchrakian, D. H.

    1987-04-01

    A manifestly O(4 p+1) invariant formulation of generalised Yang-Mills (GYM) theory on S 4p {r|r·r=1} ⊂ R 4p+1 is given, and the corresponding BPST instantons and anti-instantons are shown to be solutions of the equations of motion.

  4. Three-dimensional super Yang-Mills with unquenched flavor

    NASA Astrophysics Data System (ADS)

    Faedo, Antón F.; Mateos, David; Tarrío, Javier

    2015-07-01

    We construct analytically the gravity duals of three-dimensional, super Yang-Mills-type theories with supersymmetry coupled to N f quark flavors. The backreaction of the quarks on the color degrees of freedom is included, and corresponds on the gravity side to the backreaction of N f D6-branes on the background of N D2-branes. The D6-branes are smeared over the compact part of the geometry, which must be a six-dimensional nearly Kähler manifold in order to preserve supersymmetry. For massless quarks, the solutions flow in the IR to an AdS 4 fixed point dual to a Chern-Simons-matter theory. For light quarks the theories exhibit quasi-conformal dynamics (walking) at energy scales m q ≪ E ≪ λN f / N, with λ = g YM 2 N the 't Hooft coupling.

  5. The Development of the Gravitational and Yang-Mills Fields, and the Treatment of Accelerated Frames

    NASA Astrophysics Data System (ADS)

    Hsu, Jong-Ping; Fine, Dana

    We discuss ideas and problems regarding classical and quantum gravity, gauge theory of gravity, and space-time transformations between accelerated frames. Both Einstein's theory of gravity and Yang-Mills theory are gauge invariant. The invariance principles are at the very heart of our understanding of the physical world. This paper attempts to survey the development and to reveal problems and limitations of various formulations to gravitational and Yang-Mills fields, and to space-time transformations of accelerated frames. Gravitational force and accelerated frames are two ingredients in Einstein's thought in the period around 1907. Accelerated frames are difficult to define and are not well developed. However, one cannot claim to have a complete understanding of the physical world, if one understands flat space-time physics only from the viewpoint of the special class of inertial frames and ignores the vast class of noninertial frames. The paper highlights three aspects: (1) ideas of gravity as a Yang-Mills field, first discussed by Utiyama; (2) problems of quantum gravity, discussed by Feynman, Dyson and others; (3) space-time properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and Yang-Mills' profound thoughts present a challenge to physicists and mathematicians in the 21st century.

  6. Galactic Rotation Curves from Yang-Mills Gravity

    NASA Astrophysics Data System (ADS)

    Katz, Daniel

    2014-03-01

    Yang-Mills Gravity (YMG) is a gauge field theory based on the T4 group in flat spacetime. In its macroscopic limit, it modifies the trajectories of classical objects such that it serves as an alternative to General Relativity (GR). Since YMG is relatively new and unknown, a brief review of the general theory is given and a more comprehensive list of references is provided. In the present work, we find that the Schwarzchild-like solution to YMG supports a term like αr with constant α. This translates into an r-term in the effective gravitational potential of classical objects. We use this modified potential to predict the shape of the rotation curves of spiral galaxies, and then use data from SDSS to constrain α, which seems to be a free parameter in YMG. This work was supported the NSF's GK12 Vibes and Waves Fellowship.

  7. Einstein-Yang-Mills scattering amplitudes from scattering equations

    NASA Astrophysics Data System (ADS)

    Cachazo, Freddy; He, Song; Yuan, Ellis Ye

    2015-01-01

    We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of n massless particles are given by integrals over the positions of n points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein-Yang-Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke-Taylor-like factors of subsets of particle labels.

  8. Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

    NASA Astrophysics Data System (ADS)

    Teng, Fei; Feng, Bo

    2017-05-01

    Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with an arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.

  9. Classical Yang-Mills Mechanics: Instant vs. Light-cone Form

    SciTech Connect

    Mladenov, D.

    2010-11-25

    Two different forms of relativistic dynamics, the instant and the light-cone form, for the pure SU(2) Yang-Mills field theory in 4-dimensional Minkowski space are examined under the supposition that the gauge fields depend on the time evolution parameter only. The obtained under that restriction of gauge potential space homogeneity mechanical matrix model, sometimes called Yang-Mills classical mechanics, is systematically studied in its instant and light-cone form of dynamics using the Dirac's generalized Hamiltonian approach. In the both cases the constraint content of the obtained mechanical systems is found. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills classical mechanics has in addition to the constraints generating the SU(2) gauge transformations the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. In the instant form of dynamics it is shown that after elimination of the gauge degrees of freedom from the classical SU(2) Yang-Mills mechanics the resulting unconstrained system represents the ID{sub 3} Euler-Calogero-Moser model with a certain external fourth-order potential, whereas in the light-cone form it is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics.

  10. Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

    NASA Astrophysics Data System (ADS)

    Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

    2017-08-01

    We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS4 as R ×S3, via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τ ∈R is given by B˜a=-1/2 Ia/(R2cosh2τ ), where Ia for a =1 , 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -1/2 j (j +1 )(2 j +1 )π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

  11. On the sign problem in 2D lattice super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Catterall, Simon; Galvez, Richard; Joseph, Anosh; Mehta, Dhagash

    2012-01-01

    In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the mathcal{N} = (2, 2) and mathcal{N} = (8, 8) supersymmetric Yang-Mills theories in two dimensions for the U(N ) theories with N = 2, 3, 4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional mathcal{N} = 4 supersymmetric Yang-Mills theory.

  12. Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large-N limit of SU(N) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Bochicchio, M.

    2009-05-01

    We localize the loop equation of large-N YM theory in the anti-self-dual variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the anti-self-dual integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative anti-self-dual vortices of the Eguchi-Kawai reduction. An exact canonical beta function of Novikov-Shifman-Vainshtein-Zakharov type, that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.

  13. The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

    NASA Astrophysics Data System (ADS)

    Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto

    2015-12-01

    We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g GF 2 ˜ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.

  14. Does the lattice zero-momentum gluon propagator for pure-gauge SU(3) Yang-Mills theory vanish in the infinite-volume limit?

    SciTech Connect

    Oliveira, O.; Silva, P. J.

    2009-02-01

    The Cucchieri-Mendes bounds for the gluon propagator are discussed for the four dimensional pure-gauge SU(3) theory. Assuming a pure power law dependence on the inverse of the lattice volume, the lattice data gives a vanishing zero-momentum gluon propagator in the infinite-volume limit in agreement with the Gribov-Zwanziger horizon condition but contradicting the SU(2) analysis. The results are robust against variations of the lattice volumes and corrections to the power law. Our analysis considers also more general ansatze that, although not conclusive, open the possibility of having D(0){ne}0 in the infinite-volume limit. A solution to this puzzle requires further investigations.

  15. Cosmological coevolution of Yang-Mills fields and perfect fluids

    SciTech Connect

    Barrow, John D.; Jin, Yoshida; Maeda, Kei-ichi

    2005-11-15

    We study the coevolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis but the bound is comparatively weak with {omega}{sub YM}<0.105{omega}{sub rad}.

  16. Newtonian perturbations and the Einstein Yang Mills-dilaton equations

    NASA Astrophysics Data System (ADS)

    Oliynyk, Todd A.

    2005-06-01

    In this paper, we show that the problem of proving the existence of a countable number of solutions to the static spherically symmetric SU(2) Einstein Yang Mills-dilaton (EYMd) equations can be reduced to proving the non-existence of solutions to the linearized Yang Mills-dilaton equations (lYMd) satisfying certain asymptotic conditions. The reduction from a nonlinear to a linear problem is achieved using a Newtonian perturbation-type argument.

  17. Reconstructing cosmic acceleration from modified and nonminimal gravity: The Yang-Mills case

    SciTech Connect

    Elizalde, E.; Lopez-Revelles, A. J.

    2010-09-15

    A variant of the accelerating cosmology reconstruction program is developed for f(R) gravity and for a modified Yang-Mills/Maxwell theory. Reconstruction schemes in terms of e-foldings and by using an auxiliary scalar field are developed and carefully compared, for the case of f(R) gravity. An example of a model with a transient phantom behavior without real matter is explicitly discussed in both schemes. Further, the two reconstruction schemes are applied to the more physically interesting case of a Yang-Mills/Maxwell theory, again with explicit examples. Detailed comparison of the two schemes of reconstruction is presented also for this theory. It seems to support, as well, physical nonequivalence of the two frames.

  18. U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations in N=4 super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Jia, Yin; Huang, Rijun; Liu, Chang-Yong

    2010-09-01

    By using the Britto-Cachazo-Feng-Witten recursion relation of N=4 super Yang-Mills theory, we proved the color reflection, U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered amplitudes of N=4 super Yang-Mills theory. This proof verified the conjectured Bern-Carrasco-Johansson relations of matter fields. The proof depended only on general properties of superamplitudes. We showed also that the color reflection relation and U(1)-decoupling relation are special cases of Kleiss-Kuijf relations.

  19. Two-Dimensional Lattice for Four-Dimensional N = 4 Supersymmetric Yang-Mills

    NASA Astrophysics Data System (ADS)

    Hanada, M.; Matsuura, S.; Sugino, F.

    2011-10-01

    We construct a lattice formulation of a mass-deformed two-dimensional N = (8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N = 4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N = 4 super Yang-Mills on R^4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

  20. New perspectives on an old problem: The bending of light in Yang-Mills gravity

    NASA Astrophysics Data System (ADS)

    Cottrell, Kazuo Ota; Hsu, Jong-Ping

    Yang-Mills gravity with electromagnetism predicts, in the geometric optics limit, a value for the deflection of light by the sun which agrees closely with the reanalysis of Eddington's 1919 optical measurements done in 1979. Einstein's General Theory of Relativity, on the other hand, agrees very closely with measurements of the deflection of electromagnetic waves made in the range of radio frequencies. Since both General Relativity and Yang-Mills gravity with electromagnetism in the geometric optics limit make predictions for the optical region which fall within experimental uncertainty, it becomes important to consider the possibility of the existence of a frequency dependence in the measurement results for the deflection of light, in order to determine which theory more closely describes nature...

  1. Periodic orbits and nonintegrability of generalized classical Yang-Mills Hamiltonian systems

    SciTech Connect

    Jimenez-Lara, Lidia; Llibre, Jaume

    2011-03-15

    The averaging theory of first order is applied to study a generalized Yang-Mills system with two parameters. Two main results are proved. First, we provide sufficient conditions on the two parameters of the generalized system to guarantee the existence of continuous families of isolated periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. Second, we prove that for the nonintegrable classical Yang-Mills Hamiltonian systems, in the sense of Liouville-Arnold, which have the isolated periodic orbits found with averaging theory, cannot exist in any second first integral of class C{sup 1}. This is important because most of the results about integrability deals with analytic or meromorphic integrals of motion.

  2. Lattice super-Yang-Mills using domain wall fermions in the chiral limit

    SciTech Connect

    Giedt, Joel; Brower, Richard; Catterall, Simon; Fleming, George T.; Vranas, Pavlos

    2009-01-15

    Lattice N=1 super-Yang-Mills formulated using Ginsparg-Wilson fermions provides a rigorous nonperturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one explicit scheme for achieving this and using them we have performed large-scale Monte Carlo simulations of the theory for gauge group SU(2). We have measured the gaugino condensate, static potential, Creutz ratios, and residual mass for several values of the domain wall separation L{sub s}, four-dimensional lattice volume, and two values of the bare gauge coupling. With this data we are able to extrapolate the gaugino condensate to the chiral limit, to express it in physical units, and to establish important benchmarks for future studies of super-Yang-Mills on the lattice.

  3. A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model

    SciTech Connect

    Shimasaki, Shinji

    2008-11-23

    We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored.

  4. String scattering in flat space and a scaling limit of Yang-Mills correlators

    SciTech Connect

    Okuda, Takuya; Penedones, Joao

    2011-04-15

    We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the 2{yields}2 scattering amplitude of massless string states in type IIB superstring theory on ten-dimensional Minkowski space and a scaling limit of the N=4 super Yang-Mills four-point functions. We conjecture that this relation holds nonperturbatively and at arbitrarily high energy.

  5. Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

    SciTech Connect

    Bertin, M. C.; Pimentel, B. M.; Valcárcel, C. E.; Zambrano, G. E. R.

    2014-04-15

    We analyse the constraint structure of the topologically massive Yang-Mills theory in instant-form and null-plane dynamics via the Hamilton-Jacobi formalism. The complete set of hamiltonians that generates the dynamics of the system is obtained from the Frobenius’ integrability conditions, as well as its characteristic equations. As generators of canonical transformations, the hamiltonians are naturally linked to the generator of Lagrangian gauge transformations.

  6. Regular solutions to higher order curvature Einstein Yang Mills systems in higher dimensions

    NASA Astrophysics Data System (ADS)

    Breitenlohner, Peter; Maison, Dieter; Tchrakian, D. H.

    2005-12-01

    We study regular, static, spherically symmetric solutions of Yang Mills theories employing higher order invariants of the field strength coupled to gravity in d dimensions. We consider models with only two such invariants characterized by integers p and q. These models depend on one dimensionless parameter α leading to one-parameter families of regular solutions, obtainable by numerical solution of the corresponding boundary value problem. Much emphasis is put on an analytical understanding of the numerical results.

  7. Initial data for gravity coupled to scalar, electromagnetic, and Yang-Mills fields

    NASA Astrophysics Data System (ADS)

    Husain, Viqar

    1999-02-01

    We give Ansätze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism, or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The time-asymmetric examples are used to test Penrose's cosmic censorship inequality. We find that the inequality can be violated if only the weak energy condition holds.

  8. Maximally supersymmetric planar Yang-Mills amplitudes at five loops

    SciTech Connect

    Bern, Z.; Carrasco, J. J. M.; Johansson, H.; Kosower, D. A.

    2007-12-15

    We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for nontrivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.

  9. Yang-Mills equation for the nuclear geometrical collective model connexion

    NASA Astrophysics Data System (ADS)

    Sparks, N.; Rosensteel, G.

    2017-01-01

    The Bohr-Mottelson collective model of rotations and quadrupole vibrations is a foundational model in nuclear structure physics. A modern formulation using differential geometry of bundles builds on this legacy collective model to allow a deformation-dependent interaction between rotational and vortical degrees of freedom. The interaction is described by the bundle connexion. This article reports the Yang-Mills equation for the connexion. For a class of solutions to the Yang-Mills equation, the differential geometric collective model attains agreement between experiment and theory for the moments of inertia of deformed isotopes. More generally, the differential geometric framework applies to models of emergent phenomena in which two interacting sets of degrees of freedom must be unified.

  10. Recombination of H and He in Yang-Mills Gravity

    NASA Astrophysics Data System (ADS)

    Katz, Daniel

    2015-07-01

    We investigate some aspects of the thermal history of the early universe according to Yang-Mills Gravity (YMG); a gauge theory of gravity set in flat space-time. Specifically, equations for the ionization fractions of hydrogen and singly ionized helium during the recombination epoch are deduced analytically and then solved numerically. By considering several approximations, we find that the presence of primordial helium and its interaction with Lyman series photons has a much stronger effect on the overall free electron density in YMG than it does in the standard, General Relativity (GR)-based, model. Compared to the standard model, recombination happens over a much larger range of temperatures, although there is still a very sharp temperature of last scattering around 2000 K. The ionization history of the universe is not directly observable, but knowledge of it is necessary for CMB power spectrum calculations. Such calculations will provide another rigorous test of YMG and will be explored in detail in an upcoming paper.

  11. Non-Perturbative Yang-Mills from Supersymmetry and Strings, Or, in the Jungles of Strong Coupling

    NASA Astrophysics Data System (ADS)

    Shifman, M.

    2005-12-01

    I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.

  12. Echoing and scaling in Einstein-Yang-Mills critical collapse

    NASA Astrophysics Data System (ADS)

    Gundlach, Carsten

    1997-05-01

    We confirm recent numerical results of echoing and mass scaling in the gravitational collapse of a spherical Yang-Mills field by constructing the critical solution and its perturbations as an eigenvalue problem. Because the field equations are not scale invariant, the Yang-Mills critical solution is asymptotically, rather than exactly, self-similar, but the methods for dealing with discrete self-similarity developed for the real scalar field can be generalized. We find an echoing period Δ=0.73784+/-0.00002 and a critical exponent for the black hole mass γ=0.1964+/-0.0007.

  13. Supergravity backgrounds for four-dimensional maximally supersymmetric Yang-Mills

    NASA Astrophysics Data System (ADS)

    Maxfield, Travis

    2017-02-01

    In this note, we describe supersymmetric backgrounds for the four-dimensional maximally supersymmetric Yang-Mills theory. As an extension of the method of Festuccia and Seiberg to sixteen supercharges in four dimensions, we utilize the coupling of the gauge theory to maximally extended conformal supergravity. Included among the fields of the conformal supergravity multiplet is the complexified coupling parameter of the gauge theory; therefore, backgrounds with spacetime varying coupling — such as appear in F-theory and Janus configurations — are naturally included in this formalism. We demonstrate this with a few examples from past literature.

  14. Small coupling limit and multiple solutions to the Dirichlet problem for Yang-Mills connections in four dimensions. II

    NASA Astrophysics Data System (ADS)

    Isobe, Takeshi; Marini, Antonella

    2012-06-01

    In this paper, we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the ɛ-Dirichlet problem obtained as a variational problem for the SU(2)ɛ-Yang-Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem for the SU(2)-Yang-Mills functional with small boundary data. In the first paper of this series this non-compact variational problem is transformed into the finite-dimensional problem of finding the critical points of the function J_{ɛ }({q}), which is essentially the Yang-Mills functional evaluated on the approximate solutions, constructed via a gluing technique. In the present paper, we establish a Morse theory for J_{ɛ }({q}), by means of Ljusternik-Schnirelmann theory, thus complete the proofs of Theorems 1-3 given by Isobe and Marini ["Small coupling limit and multiple solutions to the Dirichlet Problem for Yang-Mills connections in 4 dimensions - Part I," J. Math. Phys. 53, 063706 (2012)], 10.1063/1.4728211.

  15. Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry

    NASA Technical Reports Server (NTRS)

    Hsu, J. P.

    1981-01-01

    A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.

  16. Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry

    NASA Technical Reports Server (NTRS)

    Hsu, J. P.

    1981-01-01

    A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.

  17. Warped Products and Yang-Mills Equations on Noncommutative Spaces

    NASA Astrophysics Data System (ADS)

    Zampini, Alessandro

    2015-02-01

    This paper presents a non-self-dual solution of the Yang-Mills equations on a noncommutative version of the classical , so generalizing the classical meron solution first introduced by de Alfaro et al. (Phys Lett B 65:163-166, 1976). The basic tool for that is a generalization to noncommutative spaces of the classical notion of warped products between metric spaces.

  18. Yang - Mills - Higgs equations with nonhomogeneous boundary conditions

    NASA Astrophysics Data System (ADS)

    Tafel, Jacek

    1997-01-01

    The Yang - Mills - Higgs equations in a spatially bounded subset of the Minkowski space are studied under the assumption of a temporal gauge. It is shown that the Cauchy problem for these equations is uniquely solvable (locally in time) if nonhomogeneous boundary conditions of the metallic type are imposed.

  19. Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills

    NASA Astrophysics Data System (ADS)

    Hall, John; Low, Andrew

    2014-06-01

    We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.

  20. Deconfinement and Duality of (super) Yang-Mills on Toroidially-Compactified Spacetimes for all Gauge Groups

    NASA Astrophysics Data System (ADS)

    Teeple, Brett

    I study gauge theories for any gauge group G, in particular Yang-Mills (YM) theories including super Yang-Mills (SYM) and mass deformed super Yang-Mills (SYM*), on toroidially compactified spacetimes. Each compact direction introduces r = rank( G) massive scalar fields into the theory and results in an effective potential added to the Lagrangian of the theory. The mathematics of such potentials is interesting, however important applications begin with special simple cases. The first case studied here is finite temperature super Yang-Mills where a thermal circle of size 1/T is introduced and the temperature dependence of phases of the theory can be studied including the deconfinement phase transition. Further compactification on a spatial circle of size L is useful. For small such L we are in a regime where semiclassical calculations can be performed at weak coupling. The transition is found to be mediated by the competition between non-perturbative objects including monopole-instantons and 'exotic' topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with charges in the co-root lattice of the gauge group G, as well as electrically charged W-bosons (and wino superpartners in the case of SYM) with charges in the root lattice of G.. The second case is super Yang-Mills on circle compactified spacetimes, but with softly broken supersymmetry with a small mass m for the adjoint fermion. This is interesting as there is a conjectured continuity relating this theory, and its quantum deconfining phase transition at some critical mass for the gluino, to pure Yang-Mills with a thermal deconfinement transition at some critical temperature. Furthermore, on torus compactified spacetimes, I determine a duality for all G to a 2D Coulomb gas of bions of different charges of their monopole constituents, and W-bosons of both scalar and electric charges. Aharonov-Bohm interactions exist between magnetic bions and W-bosons. New scalar

  1. Symmetric blocking and renormalization in lattice N=4 super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Giedt, Joel; Catterall, Simon

    2015-04-01

    The form of the long distance effective action of the twisted lattice N = 4 super Yang-Mills theory depends on having a real space renormalization group transformation that preserves the original lattice properties, both the symmetries and the geometric interpretation of the fields. We have found such a transformation and have exhibited its behavior through a preliminary Monte Carlo renormalization group calculation. Other results regarding the number of counterterms are also obtained by considering rescalings of the lattice fields. Supported by Department of Energy, Office of Science, Office of High Energy Physics Grants DE-FG02-08ER41575 and SC0009998.

  2. Classical Yang-Mills Black Hole Hair in Anti-de Sitter Space

    NASA Astrophysics Data System (ADS)

    Winstanley, E.

    The properties of hairy black holes in Einstein-Yang-Mills (EYM) theory are reviewed, focusing on spherically symmetric solutions. In particular, in asymptotically anti-de Sitter space (adS) stable black hole hair is known to exist for frak su(2) EYM. We review recent work in which it is shown that stable hair also exists in frak su(N) EYM for arbitrary N, so that there is no upper limit on how much stable hair a black hole in adS can possess.

  3. On the functional renormalization group approach for Yang-Mills fields

    NASA Astrophysics Data System (ADS)

    Lavrov, Peter M.; Shapiro, Ilya L.

    2013-06-01

    We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of S-matrix.

  4. Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter

    NASA Astrophysics Data System (ADS)

    Brodbeck, Othmar; Heusler, Markus

    1997-11-01

    Using the Kaluza-Klein structure of stationary spacetimes, a framework for analyzing stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter fields is presented. It is shown that the perturbations giving rise to a nonvanishing ADM angular momentum are governed by a self-adjoint system of equations for a set of gauge-invariant scalar amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes arise generically in self-gravitating non-Abelian gauge theories with bosonic matter, whereas, in general, soliton solutions do not have rotating counterparts.

  5. The nuclear geometric Yang-Mills equation for incompressible nuclei

    NASA Astrophysics Data System (ADS)

    Sparks, Nicholas; Rosensteel, George

    2016-09-01

    The geometric Yang-Mills equation for the Bohr-Mottelson collective model provides a way of relating angular momentum degrees of freedom to the internal (Kelvin circulation) degrees of freedom. It is well known that nuclei are highly incompressible. The correct mathematical description for nuclear incompressibility involves an equation of constraint for constant volume. An alternative yet equivalent description involves treating this constraint in a purely differential geometric way. The relationship between these two seemingly different approaches is explored here.

  6. Gravity and Yang-Mills amplitude relations

    SciTech Connect

    Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Soendergaard, Thomas; FengBo

    2010-11-15

    Using only general features of the S matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.

  7. Three-dimensional super Yang-Mills with compressible quark matter

    NASA Astrophysics Data System (ADS)

    Faedo, Antón F.; Kundu, Arnab; Mateos, David; Pantelidou, Christiana; Tarrío, Javier

    2016-03-01

    We construct the gravity dual of three-dimensional, SU(N c) super Yang-Mills theory with N f flavors of dynamical quarks in the presence of a non-zero quark density N q. The supergravity solutions include the backreaction of N c color D2-branes and N f flavor D6-branes with N q units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ = N c 2 N q/ λ 2 N f 4 , with λ = g YM 2 N c the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z = 5 and θ = 1, respectively. If ρ ≪ 1 then at intermediate energies there is also an approximate AdS4 region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass M q the physics depends non-trivially on ρ and M q N c /λ N f.

  8. Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models

    NASA Astrophysics Data System (ADS)

    Cembranos, Jose A. R.; Gigante Valcarcel, Jorge

    2017-07-01

    In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular correspondence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. The applicability of the method is divided into two approaches: one associated with the Lorentz group S O (1 ,n -1 ) of the space-time rotations, and another one with its subgroup S O (n -2 ). Solutions for both cases are presented by the explicit use of this correspondence and, interestingly, for the last one by imposing on our ansatz the same kind of rotation and reflection symmetry properties as for a nonvanishing space-time torsion. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them, and it may be used in future research to find other exact solutions within this theory.

  9. Yang-Mills Field as a Subset of Covariant Derivative -- a Unified Yang-Mills Field and Higgs Field

    NASA Astrophysics Data System (ADS)

    Gan, Woon Siong

    2014-04-01

    A different approach using the covariant derivative is used to derive the Yang-Mills field. This avoids the weakness of resulting massless particles. Covariant derivative is also used to derive the Higgs field. A detailed mass acquisition mechanism for matter particles and force particles is given for the Higgs field. This paves the way towards a unified Yang-Mills field and Higgs field. We show that the Yang-Mills field is a special case of the unified field when the temperature is above the critical temperature of the spontaneous symmetry breaking (SSB). SSB has a broader implication that it can be extended to all particles in the universe. Higgs boson is a product of SSB and it causes the Big Bang points to the role of SSB in the Big Bang creation of the universe and this gives support to the proposed superfluid model for the particles of the universe beyond the Standard Model. The critical temperature for SSB is equivalent to the extremely high temperature which occurs during the Big Bang.

  10. Yang Mills condensate dark energy coupled with matter and radiation

    NASA Astrophysics Data System (ADS)

    Zhang, Y.; Xia, T. Y.; Zhao, W.

    2007-07-01

    The coincidence problem is studied for the dark energy model of effective Yang Mills condensate (YMC) in a flat expanding universe during the matter-dominated stage. The YMC energy ρy(t) is taken to represent the dark energy, which is coupled either with the matter ρm(t), or with both the matter and the radiation components ρr(t). The effective YM Lagrangian is completely determined by the quantum field theory up to 1-loop order with an energy scale ~10-3 eV as a model parameter, and for each coupling, there is an extra model parameter. We have studied extensively the coupling models: the YMC decaying into the matter and the radiation; or vice versa the matter and radiation decaying into the YMC. It is found that, starting from the equality of radiation-matter ρmi = ρri, for a wide range of initial conditions of ρyi = (10-10, 10-2)ρmi, the models have a scaling solution during the early stages, and the YMC levels off and becomes dominant at late time, and the present state with Ωy sime 0.7, Ωm sime 0.3 and Ωr sime 10-5 is always achieved. If the YMC decays into a component, then this component also levels off later and approaches a constant value asymptotically, and the equation of state (EoS) of the YMC wy = ρy/py crosses over -1 and takes the value wy sime -1.1 at z = 0. If the matter and radiation decay into the YMC, then ρm(t) ~ a(t)-3 and ρr(t) ~ a(t)-4 approximately for all the time, and wy approaches -1 but does not cross over -1. We have also demonstrated that, at t → ∞, the coupled dynamics for (ρy(t), ρm(t), ρr(t)) is a stable attractor. Therefore, under generic circumstances, the existence of the scaling solution during the early stages and the subsequential exit from the scaling regime around z sime (0.3 0.5) are inevitable. Thus the coincidence problem can be naturally solved in the YMC dark energy models.

  11. Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops

    SciTech Connect

    Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.; /Moscow State U.

    2005-05-27

    We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

  12. Smallest 3d hyperbolic manifolds via simple 3d theories

    NASA Astrophysics Data System (ADS)

    Gang, Dongmin; Tachikawa, Yuji; Yonekura, Kazuya

    2017-09-01

    We provide strong pieces of evidence that mathematics of three-dimensional hyperbolic manifolds of the first, second and third smallest volume are captured by the physics of three-dimensional theories composed of a complex boson and a Dirac fermion, both of a unit charge, coupled to a U(1) gauge field with the Chern-Simons levels -5 /2 , -7 /2 and -3 /2 , respectively.

  13. Small coupling limit and multiple solutions to the Dirichlet problem for Yang-Mills connections in four dimensions. I

    NASA Astrophysics Data System (ADS)

    Isobe, Takeshi; Marini, Antonella

    2012-06-01

    In this paper and its sequel (Part II), we analyze the space of solutions to the ɛ-Dirichlet problem for the Yang-Mills equations on the four-dimensional disk, for small values of the coupling constant ɛ. These are in 1-1 correspondence with solutions to the Dirichlet problem for Yang-Mills, for small boundary data ɛA0. We establish a Morse theory for this non-compact variational problem and prove the existence of multiple solutions, and, also, non minimal ones. Here, we describe the problem, state the main theorems and do the first part of the proof. This consists in making the problem finite dimensional, by seeking solutions approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. By introducing an auxiliary equation, we solve the problem orthogonally to the space of the approximate solutions.

  14. Quantum cosmological Friedman models with a massive Yang-Mills field

    NASA Astrophysics Data System (ADS)

    Gerhardt, Claus

    2009-07-01

    We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case, the mass of the Yang-Mills field assumes the role of the eigenvalue.

  15. A gravitating Yang-Mills instanton

    NASA Astrophysics Data System (ADS)

    Cano, Pablo A.; Ortín, Tomás; Ramírez, Pedro F.

    2017-07-01

    We present an asymptotically flat, spherically symmetric, static, globally regular and horizonless solution of SU(2)-gauged N=1 , d = 5 supergravity. The SU(2) gauge field is that of the BPST instanton. We argue that this solution, analogous to the global monopoles found in d = 4 N=2 and N=4 gauged supergravities, describes the field of a single string-theory object which does not contribute to the entropy of black holes when we add it to them and show that it is, indeed, the dimensional reduction on T5 of the gauge 5-brane. We investigate how the energy of the solution is concentrated as a function of the instanton's scale showing that it never violates the hoop conjecture although the curvature grows unboundedly in the zero scale limit.

  16. Constructing the tree-level Yang-Mills S-matrix using complex factorization

    NASA Astrophysics Data System (ADS)

    Schuster, Philip C.; Toro, Natalia

    2009-06-01

    A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants — these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~ 1/z2.

  17. Relations for Einstein-Yang-Mills amplitudes from the CHY representation

    NASA Astrophysics Data System (ADS)

    de la Cruz, Leonardo; Kniss, Alexander; Weinzierl, Stefan

    2017-04-01

    We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and (n - 1) gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with n gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with r gravitons and (n - r) gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with n gauge bosons. We present a general formula for this case.

  18. Yang-Mills condensate as dark energy: A nonperturbative approach

    NASA Astrophysics Data System (ADS)

    Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia

    2016-02-01

    Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

  19. Einstein-scalar-Yang-Mills black holes: a thermodynamical approach

    NASA Astrophysics Data System (ADS)

    Biswas, Ritabrata

    2013-12-01

    We try to find out the nature of different thermodynamical parameters for a black hole solution drawn for a special case in Einstein-Scalar-Yang-Mills gravity. Whether a phase transition occurs for the solution or not is a matter of interest. The nature of the phase transition is tried to understand. Ruppeiner metric and the corresponding Ricci scalar is constructed. It is noticed that the metric is not of positive Ricci for all the parametric values and there exist(s) point(s) in thermodynamic space where the Ricci scalar becomes zero.

  20. 3D string theory and Umbral moonshine

    NASA Astrophysics Data System (ADS)

    Kachru, Shamit; Paquette, Natalie M.; Volpato, Roberto

    2017-10-01

    The simplest string theory compactifications to 3D with 16 supercharges—the heterotic string on T 7, and type II strings on K3 × T3 —are related by U-duality, and share a moduli space of vacua parametrized by O(8, 24;{{ Z}}) ~\\backslash ~O(8, 24)~ /~ (O(8) × O(24)) . One can think of this as the moduli space of even, self-dual 32-dimensional lattices with signature (8,24). At 24 special points in moduli space, the lattice splits as Γ8, 0 \\oplus Γ0, 24 . Γ0, 24 can be the Leech lattice or any of 23 Niemeier lattices, while Γ8, 0 is the E 8 root lattice. We show that starting from this observation, one can find a precise connection between the Umbral groups and type IIA string theory on K3. This may provide a natural physical starting point for understanding Mathieu and Umbral moonshine. The maximal unbroken subgroups of Umbral groups in 6D (or any other limit) are those obtained by starting at the associated Niemeier point and moving in moduli space while preserving the largest possible subgroup of the Umbral group. To illustrate the action of these symmetries on BPS states, we discuss the computation of certain protected four-derivative terms in the effective field theory, and recover facts about the spectrum and symmetry representations of 1/2-BPS states.

  1. Yang-Mills matrix mechanics and quantum phases

    NASA Astrophysics Data System (ADS)

    Pandey, Mahul; Vaidya, Sachindeo

    The SU(2) Yang-Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The SU(2) Yang-Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

  2. Wilson loops in 3d {N} = 4 SQCD from Fermi gas

    NASA Astrophysics Data System (ADS)

    Okuyama, Kazumi

    2016-11-01

    We study 1/2 BPS Wilson loops in 3d {N} = 4 U( N ) Yang-Mills theory with one adjoint and N f fundamental hypermultiplets from the Fermi gas approach. By numerical fitting, we find the first few worldsheet instanton corrections to the Wilson loops with winding numbers 1, 2 and 3. We verify that our Fermi gas results are consistent with the matrix model results in the planar limit.

  3. Gravitating Vortices, Cosmic Strings, and the Kähler-Yang-Mills Equations

    NASA Astrophysics Data System (ADS)

    Álvarez-Cónsul, Luis; Garcia-Fernandez, Mario; García-Prada, Oscar

    2017-04-01

    In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi.

  4. Higher-dimensional thin-shell wormholes in Einstein-Yang-Mills-Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Mazharimousavi, S. Habib; Halilsoy, M.; Amirabi, Z.

    2011-01-01

    We present thin-shell wormhole solutions in the Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) theory in higher dimensions d >= 5. Exact black hole solutions are employed for this purpose where the radius of the thin shell lies outside the event horizon. For some reasons the cases d = 5 and d > 5 are treated separately. The surface energy-momentum of the thin shell creates surface pressures to resist against collapse and rendering stable wormholes possible. We test the stability of the wormholes against spherical perturbations through a linear energy-pressure relation and plot stability regions. Apart from this restricted stability we investigate the possibility of normal (i.e. non-exotic) matter which satisfies the energy conditions. For negative values of the Gauss-Bonnet (GB) parameter we obtain such physical wormholes.

  5. a Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills Framework

    NASA Astrophysics Data System (ADS)

    Hsu, Jong-Ping

    Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include spacetime translational group T(4), whose generators Tμ ( = ∂/∂xμ) do not have constant matrix representations. By gauging T(4) × SU(2) × U(1) in flat spacetime, we have a new tensor field ϕμν which universally couples to all particles and anti-particles with the same constant g, which has the dimension of length. In this unified model, the T(4) gauge symmetry dictates that all wave equations of fermions, massive bosons and the photon in flat spacetime reduce to a Hamilton-Jacobi equation with the same "effective Riemann metric tensor" in the geometric-optics limit. Consequently, the results are consistent with experiments. We demonstrated that the T(4) gravitational gauge field can be quantized in inertial frames.

  6. Chiral splitting and N=4 Einstein-Yang-Mills tree amplitudes in 4d

    NASA Astrophysics Data System (ADS)

    Roehrig, Kai A.

    2017-08-01

    We present a world-sheet formula for all tree level scattering amplitudes, in all trace sectors, of four dimensional N\\le 4 supersymmetric Einstein-Yang-Mills theory, based on the refined scattering equations. This generalizes previously known formulas for all-trace purely bosonic, or supersymmetric single-trace amplitudes. We find this formula by applying a new chiral splitting formula for all CHY Pfaffians in 4d, into two determinants, of positive and negative helicity respectively. The splitting of CHY Pfaffians is shown to be a special case of the splitting of TM valued fermion correlators on the sphere, which does not require the scattering equations to hold, and is a consequence of the isomorphism TM˜eq S+⊗ S- between the tangent bundle of Minkowski space and the left- and right-handed spin bundles. We present and prove this general splitting formula.

  7. Regge meets collinear in strongly-coupled N=4 super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Sprenger, Martin

    2017-01-01

    We revisit the calculation of the six-gluon remainder function in planar N=4 super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in [1], which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.

  8. Hydrodynamics of the Polyakov line in SU(Nc) Yang-Mills

    DOE PAGES

    Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail

    2015-12-08

    We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite Nc for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of Nc, and are consistent with the string model results at Nc = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is capturedmore » by a hydrodynamical instanton. An estimate of the probability of formation of a Z(Nc)bubble using a piece-wise sound wave is suggested.« less

  9. 2-loop quantum Yang Mills condensate as dark energy

    NASA Astrophysics Data System (ADS)

    Xia, T. Y.; Zhang, Y.

    2007-11-01

    In seeking a model solving the coincidence problem, the effective Yang Mills condensate (YMC) is an alternative candidate for dark energy. A study is made for the model up to the 2-loop order of quantum corrections. It is found that, like in the 1-loop model, for generic initial conditions during the radiation era, there is always a desired tracking solution, yielding the current status Ω≃0.73 and Ω≃0.27. As the time t→∞ the dynamics is a stable attractor. Thus the model naturally solves the coincidence problem of dark energy. Moreover, if YMC decays into matter, its equation of state (EoS) crosses -1 and takes w˜-1.1, as indicated by the recent observations.

  10. 3D Virtual Reality Check: Learner Engagement and Constructivist Theory

    ERIC Educational Resources Information Center

    Bair, Richard A.

    2013-01-01

    The inclusion of three-dimensional (3D) virtual tools has created a need to communicate the engagement of 3D tools and specify learning gains that educators and the institutions, which are funding 3D tools, can expect. A review of literature demonstrates that specific models and theories for 3D Virtual Reality (VR) learning do not exist "per…

  11. 3D Virtual Reality Check: Learner Engagement and Constructivist Theory

    ERIC Educational Resources Information Center

    Bair, Richard A.

    2013-01-01

    The inclusion of three-dimensional (3D) virtual tools has created a need to communicate the engagement of 3D tools and specify learning gains that educators and the institutions, which are funding 3D tools, can expect. A review of literature demonstrates that specific models and theories for 3D Virtual Reality (VR) learning do not exist "per…

  12. Unification Yang-Mills Groups and Representations with CP as a Gauge Symmetry

    NASA Astrophysics Data System (ADS)

    Zhang, Huazhong

    We investigate more generally the possible unification Yang-Mills groups GYM and representations with CP as a gauge symmetry. Besides the possible Yang-Mills groups E8, E7, SO(2n + 1), SO(4n), SP(2n), G2 or F4 (or a product of them) which only allow self-contragredient representations, we present other unification groups GYM and representations which may allow CP as a gauge symmetry. These include especially SU(N) containing Weyl fermions and their CP conjugates from low energy spectra in a basic irreducible representation (IR). Such an example is the 496-dimensional basic IR (on antisymmetric tensors of rank two) of SU(32) containing SO(32) as a subgroup in the adjoint IR, or SU(248) in a fundamental IR containing E8 as a subgroup in the adjoint IR. Our consideration also leads to the construction of a physical operator (CP) intrinsically as an inner automorphism of order higher than two for the unification group. We have also generalized the possible groups as unification GYM to include nonsemisimple Lie groups with CP arising as a gauge symmetry. In this case with U(1) ideals in the GYM, we found that the UY(1) for weak hypercharge in the standard model or a U(1) gauge symmetry at low energies in general is traceless. Possible relevance to superstring theory is also briefly discussed. We expect that our results may open new alternatives for unified model building, especially with deeper or more generalized understanding of anomaly-free theories.

  13. Gravitational contributions to the running Yang-Mills coupling in large extra-dimensional brane worlds

    NASA Astrophysics Data System (ADS)

    Ebert, Dietmar; Plefka, Jan; Rodigast, Andreas

    2009-02-01

    We study the question of a modification of the running gauge coupling of Yang-Mills theories due to quantum gravitational effects in a compact large extra dimensional brane world scenario with a low energy quantum gravity scale. The ADD scenario is applied for a D = d+δ dimensional space-time in which gravitons freely propagate, whereas the non-abelian gauge fields are confined to a d-dimensional brane. The extra dimensions are taken to be toroidal and the transverse fluctuation modes (branons) of the brane are taken into account. On this basis we have calculated the one-loop corrections due to virtual Kaluza-Klein graviton and branon modes for the gluon two- and three-point functions in an effective field theory treatment. Applying momentum cut-off regularization we find that for a d = 4 brane the leading gravitational divergencies cancel irrespective of the number of extra dimensions δ, generalizing previous results in the absence of extra-dimensions. Hence, again the Yang-Mills β-function receives no gravitational corrections at one-loop. This is no longer true in a `universal' extra dimensional scenario with a d > 4 dimensional brane. Moreover, the subleading power-law gravitational divergencies induce higher-dimensional counterterms, which we establish in our scheme. Interestingly, for d = 4 these gravitationally induced counterterms are of the form recently considered in non-abelian Lee-Wick extensions of the standard model—now with a possible mass scale in the TeV range due to the presence of large extra dimensions.

  14. Conformally flat Einstein-Yang-Mills-Higgs solutions with spherical symmetry

    SciTech Connect

    Mondaini, R.P.; Santos, N.O.

    1983-10-15

    We solve the Einstein-Yang-Mills-Higgs equations in a conformally flat metric with spherical symmetry. Two solutions are obtained corresponding to magnetic monopoles in the Higgs vacuum and outside of it.

  15. Supergravity coupled to chiral matter at one loop. II. Chiral and Yang-Mills matter

    SciTech Connect

    Gaillard, M.K.; Jain, V.; Saririan, K.

    1997-01-01

    We present the full calculation of the divergent one-loop contribution to the effective boson Lagrangian for supergravity, including the Yang-Mills sector and the helicity-odd operators that arise from integration over fermion fields. The only restriction is on the Yang-Mills kinetic energy normalization function, which is taken diagonal in gauge indices, as in models obtained from superstrings. {copyright} {ital 1997} {ital The American Physical Society}

  16. General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework or From Bianchi identities to twisted Courant algebroids

    NASA Astrophysics Data System (ADS)

    Grützmann, Melchior; Strobl, Thomas

    2015-10-01

    Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.

  17. Unitarity problems in 3D gravity theories

    NASA Astrophysics Data System (ADS)

    Alkac, Gokhan; Basanisi, Luca; Kilicarslan, Ercan; Tekin, Bayram

    2017-07-01

    We revisit the problem of the bulk-boundary unitarity clash in 2 +1 -dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from perturbative log-modes with negative energies inducing a nonunitary logarithmic boundary field theory. We show here that any f (R ) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity—originally constructed in a first-order formulation—and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative-energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.

  18. Causality in 3D massive gravity theories

    NASA Astrophysics Data System (ADS)

    Edelstein, José D.; Giribet, Gaston; Gómez, Carolina; Kilicarslan, Ercan; Leoni, Matías; Tekin, Bayram

    2017-05-01

    We study the constraints coming from the local causality requirement in various 2 +1 dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity noninvariant massive degree of freedom, and in new massive gravity, with two massive spin-2 degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.

  19. Gauge coupling field, currents, anomalies and N = 1 super-Yang-Mills effective actions

    NASA Astrophysics Data System (ADS)

    Ambrosetti, Nicola; Arnold, Daniel; Derendinger, Jean-Pierre; Hartong, Jelle

    2017-02-01

    Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N = 1 super-Yang-Mills theory fully compatible with the expected all-order behavior or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ β function from algebraic arguments only. The extension of results to N = 2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16B +16F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.

  20. On the ground state of Yang-Mills theory

    SciTech Connect

    Bakry, Ahmed S.; Leinweber, Derek B.; Williams, Anthony G.

    2011-08-15

    Highlights: > The ground state overlap for sets of meson potential trial states is measured. > Non-uniform gluonic distributions are probed via Wilson loop operator. > The locally UV-regulated flux-tube operators can optimize the ground state overlap. - Abstract: We investigate the overlap of the ground state meson potential with sets of mesonic-trial wave functions corresponding to different gluonic distributions. We probe the transverse structure of the flux tube through the creation of non-uniform smearing profiles for the string of glue connecting two color sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube operators are found to optimize the overlap with the ground state and display interesting features in the ground state overlap.

  1. Ice limit of Coulomb gauge Yang-Mills theory

    SciTech Connect

    Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.

    2008-10-01

    In this paper we describe gauge invariant multiquark states generalizing the path integral framework developed by Parrinello, Jona-Lasinio, and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is illustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark-antiquark potential.

  2. Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts

    NASA Astrophysics Data System (ADS)

    Boels, Rutger H.; Isermann, Reinke Sven

    2012-03-01

    This article studies methods to obtain relations for scattering amplitudes at the loop level, with concrete examples at one loop. These methods originate in the analysis of large so-called Britto-Cachazo-Feng-Witten shifts of tree level amplitudes and loop level integrands. In particular BCFW shifts for particles which are not color adjacent and some particular generalizations of this situation are analyzed in some detail in four and higher dimensions. For generic non-adjacent shifts our results are independent of loop order for integrands and hold for generic minimally coupled gauge theories with possible scalar potential and Yukawa terms. By a standard argument this result indicates a generalization of the Bern-Carrasco-Johansson relations for tree level amplitudes exists to the integrand at all loop levels. A concrete relation is presented at one loop. Furthermore, inspired by results in QED it is shown that the results on generalized BCFW shifts of tree level amplitudes imply relations for the so-called rational, bubble and triangle terms of one loop amplitudes in pure Yang-Mills theory. Bubble and triangle terms for instance are shown to obey a five photon decoupling identity, while a three photon decoupling identity is demonstrated for the rational terms. Along the same lines recently conjectured relations for helicity equal amplitudes at one loop are shown to generalize to helicity independent relations for the massive box coefficient of the rational terms.

  3. Nonminimal Isotropic Cosmological Model with Yang-Mills and Higgs Fields

    NASA Astrophysics Data System (ADS)

    Balakin, Alexander B.; Dehnen, Heinz; Zayats, Alexei E.

    We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six coupling parameters. The first three parameters relate to the nonminimal coupling of a non-Abelian gauge field and a gravity field, the next two parameters describe the so-called derivative nonminimal coupling of a scalar multiplet with a gravity field, and the sixth parameter introduces the standard coupling of a scalar field with a Ricci scalar. The formulated six-parameter nonminimal Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special choice of the coupling parameters. The nonminimally extended Yang-Mills and Higgs equations are satisfied for arbitrary gauge and scalar fields, when the coupling parameters are specifically related to the curvature constant of the isotropic space-time. Based on this special exact solution, we discuss the problem of a hidden anisotropy of the Yang-Mills field, and give an explicit example, when the nonminimal coupling effectively screens the anisotropy induced by the Yang-Mills field and thus restores the isotropy of the model.

  4. How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

    NASA Astrophysics Data System (ADS)

    Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.

    2017-07-01

    We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions d →2 . Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, 2 αF=2 -d and 2 αG=d at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

  5. Massive Yang-Mills for vector and axial-vector spectral functions at finite temperature

    NASA Astrophysics Data System (ADS)

    Hohler, Paul M.; Rapp, Ralf

    2016-05-01

    The hadronic mechanism which leads to chiral symmetry restoration is explored in the context of the ρπa1 system using Massive Yang-Mills, a hadronic effective theory which governs their microscopic interactions. In this approach, vector and axial-vector mesons are implemented as gauge bosons of a local chiral gauge group. We have previously shown that this model can describe the experimentally measured vector and axial-vector spectral functions in vacuum. Here, we carry the analysis to finite temperatures by evaluating medium effects in a pion gas and calculating thermal spectral functions. We find that the spectral peaks in both channels broaden along with a noticeable downward mass shift in the a1 spectral peak and negligible movement of the ρ peak. The approach toward spectral function degeneracy is accompanied by a reduction of chiral order parameters, i.e., the pion decay constant and scalar condensate. Our findings suggest a mechanism where the chiral mass splitting induced in vacuum is burned off. We explore this mechanism and identify future investigations which can further test it.

  6. Parametric instability of classical Yang-Mills fields in a color magnetic background

    NASA Astrophysics Data System (ADS)

    Tsutsui, Shoichiro; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira

    2015-04-01

    We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a nonexpanding geometry for elucidating the earliest stage dynamics of ultrarelativistic heavy-ion collisions. The background field configuration considered in this article is spatially homogeneous and temporally periodic and is introduced by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the (pz,pT) plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for |p |≤√{B } is similar to a Nielsen-Olesen instability. Moreover, some of the instability bands are found to emerge not only in the low-momentum but also in the high-momentum region, typically of the order of the saturation momentum as |p |˜√{B }˜Qs .

  7. The temperature-dependent Yang-Mills trace anomaly as a function of the mass gap

    NASA Astrophysics Data System (ADS)

    Gogokhia, V.; Shurgaia, A.; Vasúth, M.

    2016-10-01

    The trace anomaly or, equivalently, the interaction measure is an important thermodynamic quantity/observable, since it is very sensitive to the non-perturbative effects in the gluon plasma. It has been calculated and its analytic and asymptotic properties have been investigated with the combined force of analytic and lattice approaches to the SU(3) Yang-Mills (YM) quantum gauge theory at finite temperature. The first one is based on the effective potential approach for composite operators properly generalized to finite temperature. This makes it possible to introduce into this formalism a dependence on the mass gap Δ2, which is responsible for the large-scale dynamical structure of the QCD ground state. The gluon plasma pressure as a function of the mass gap adjusted by this approach to the corresponding lattice data is shown to be a continuously growing function of temperature T in the whole temperature range [0,∞) with the correct Stefan-Boltzmann limit at very high temperature. The corresponding trace anomaly has a finite jump discontinuity at some characteristic temperature Tc = 266.5MeV with latent heat ɛLH = 1.41. This is a firm evidence of the first-order phase transition in SU(3) pure gluon plasma. It is exponentially suppressed below Tc and has a complicated and rather different dependence on the mass gap and temperature across Tc. In the very high temperature limit its non-perturbative part has a power-type fall off.

  8. The Temperature-Dependent Yang-Mills Trace Anomaly as a Function of the Mass Gap

    NASA Astrophysics Data System (ADS)

    Gogokhia, V.; Shurgaia, A.; Vasúth, M.

    The trace anomaly or, equivalently, the interaction measure is an important thermodynamic quantity/observable, since it is very sensitive to the nonperturbative effects in the gluon plasma. It has been calculated and its analytic and asymptotic properties have been investigated with the combined force of analytic and lattice approaches to the SU(3) Yang-Mills (YM) quantum gauge theory at finite temperature. The first one is based on the effective potential approach for composite operators properly generalized to finite temperature. This makes it possible to introduce into this formalism a dependence on the mass gap Δ2, which is responsible for the large-scale dynamical structure of the QCD ground state. The gluon plasma pressure as a function of the mass gap adjusted by this approach to the corresponding lattice data is shown to be a continuously growing function of temperature T in the whole temperature range [0,∞) with the correct Stefan-Boltzmann limit at very high temperature. The corresponding trace anomaly has a finite jump discontinuity at some characteristic temperature Tc = 266.5 MeV with latent heat ∈LH = 1.41. This is a firm evidence of the first-order phase transition in SU(3) pure gluon plasma. It is exponentially suppressed below Tc and has a complicated and rather different dependence on the mass gap and temperature across Tc. In the very high temperature limit its non-perturbative part has a power-type fall off.

  9. A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity

    NASA Astrophysics Data System (ADS)

    Dengiz, Suat

    2017-08-01

    We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.

  10. Explicit derivation of Yang-Mills self-dual solutions on non-commutative harmonic space

    NASA Astrophysics Data System (ADS)

    Belhaj, A.; Hssaini, M.; Sahraoui, E. M.; Saidi, E. H.

    2001-06-01

    We develop the non-commutative harmonic space (NHS) analysis to study the problem of solving the nonlinear constraint equations of non-commutative Yang-Mills self-duality in four dimensions. We show that this space, denoted also as NHS(η,θ), has two SU(2) isovector deformations η(ij) and θ(ij) parametrizing, respectively, two non-commutative harmonic subspaces NHS(η,0) and NHS(0, θ) used to study the self-dual and anti self-dual non-commutative Yang-Mills solutions. We reformulate the Yang-Mills self-dual constraint equations on NHS(η,0) by extending the idea of harmonic analyticity to linearize them. We then give a perturbative self-dual solution recovering the ordinary one. Finally, we present the explicit computation of an exact self-dual solution.

  11. - criticality of AdS black hole in the Einstein-Maxwell-power-Yang-Mills gravity

    NASA Astrophysics Data System (ADS)

    Zhang, Ming; Yang, Zhan-Ying; Zou, De-Cheng; Xu, Wei; Yue, Rui-Hong

    2015-02-01

    We study the - critical behaivor of N-dimensional AdS black holes in Einstein-Maxwell-power-Yang-Mills gravity. Our results show the existence of the Van der Waals like small-large black hole phase transitions when taking some special values of charges of the Maxwell and Yang-Mills fields. Further to calculate the critical exponents of the black holes at the critical point, we find that they are the same as those in the Van der Waals liquid-gas system.

  12. Neutrino oscillation, finite self-mass and general Yang-Mills symmetry

    NASA Astrophysics Data System (ADS)

    Hsu, Jong-Ping

    2016-10-01

    The conservation of lepton number is assumed to be associated with a general Yang-Mills (gYM) symmetry. New transformations involve (Lorentz) vector gauge functions and characteristic phase functions, and they form a group. General Yang-Mills fields are associated with new fourth-order equations and linear potentials. Lepton self-masses turn out to be finite and proportional to the inverse of lepton masses, which implies that neutrinos should have nonzero masses. Thus, gYM symmetry could provide an understanding of neutrino oscillations and suggests that neutrinos with masses and very weak leptonic force may play a role in dark matter.

  13. Superspace gauge fixing in Yang-Mills matter-coupled conformal supergravity

    NASA Astrophysics Data System (ADS)

    Kugo, Taichiro; Yokokura, Ryo; Yoshioka, Koichi

    2016-09-01

    In D=4, N=1 conformal superspace, the Yang-Mills matter-coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kähler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincaré supergravity: one via the superconformal component formalism and the other via the Poincaré superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.

  14. Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction

    SciTech Connect

    Cook, Martin N. H.; Rodrigues, Joao P.

    2008-09-15

    We consider the large N spectrum of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction. In a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity, the difference equation associated with the Yang-Mills interaction is derived and solved exactly for two impurities. In this case, the full string tension corrected spectrum depends on two momenta. For a specific value of one of these momenta, the spectrum has the same structure as that of giant magnon bound states. States with general number of impurities are also discussed.

  15. A hyperboloidal study of tail decay rates for scalar and Yang Mills fields

    NASA Astrophysics Data System (ADS)

    Zenginoğlu, Anıl

    2008-09-01

    We investigate the asymptotic behavior of spherically symmetric solutions to scalar wave and Yang Mills equations on a Schwarzschild background. The studies demonstrate the astrophysical relevance of null infinity in predicting radiation signals for gravitational wave detectors and show how test fields on unbounded domains in black hole spacetimes can be simulated conveniently by numerically solving hyperboloidal initial value problems.

  16. An L2-isolation theorem for Yang-Mills fields on Kähler surfaces

    NASA Astrophysics Data System (ADS)

    Huang, Teng

    2017-02-01

    We prove an L2 energy gap result for Yang-Mills connections on principal G-bundles over compact Kähler surfaces with positive scalar curvature. We prove related results for compact simply-connected Calabi-Yau 2-folds.

  17. The Coulomb Branch of 3d N= 4 Theories

    NASA Astrophysics Data System (ADS)

    Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide

    2017-09-01

    We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.

  18. 3D quantum gravity and effective noncommutative quantum field theory.

    PubMed

    Freidel, Laurent; Livine, Etera R

    2006-06-09

    We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

  19. Yang-Mills instantons sitting on a Ricci-flat worldspace of double D4-branes

    SciTech Connect

    Kim, Hongsu; Yoon, Yongsung

    2001-06-15

    Thus far, there seem to be no complete criteria that can settle the issue as to what the correct generalization of the Dirac-Born-Infeld (DBI) action, describing the low-energy dynamics of the D-branes, to the non-Abelian case would be. According to recent suggestions, one might pass the issue of worldvolume solitons from an Abelian to non-Abelian setting by considering the stack of multiple, coincident D-branes and use it as a guideline to construct or censor the relevant non-Abelian version of the DBI action. In this spirit, here we are interested in the explicit construction of SU(2) Yang-Mills (YM) instanton solutions in the background geometry of two coincident probe D4-brane worldspaces, particularly when the metric of the target spacetime in which the probe branes are embedded is given by the Ricci-flat, magnetic extremal 4-brane solution in type IIA supergravity theory with its worldspace metric being given by that of Taub{endash}Newman-Unti-Tamburino (NUT) and Eguchi-Hanson solutions, the two best-known gravitational instantons. Then we demonstrate that, with this YM instanton-gravitational instanton configuration on the probe D4-brane worldvolume, the energy of the probe branes attains its minimum value and hence enjoys a stable state provided one employs Tseytlin's non-Abelian DBI action for the description of multiple probe D-branes. In this way, we support the arguments in the literature in favor of Tseytlin's proposal for the non-Abelian DBI action.

  20. 3D RISM theory with fast reciprocal-space electrostatics

    SciTech Connect

    Heil, Jochen; Kast, Stefan M.

    2015-03-21

    The calculation of electrostatic solute-solvent interactions in 3D RISM (“three-dimensional reference interaction site model”) integral equation theory is recast in a form that allows for a computational treatment analogous to the “particle-mesh Ewald” formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.

  1. Supersymmetric Yang-Mills fields as an integrable system and connections with other non-linear systems

    SciTech Connect

    Chau, L.L.

    1983-01-01

    Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.

  2. A Yang-Mills field on the extremal Reissner-Nordström black hole

    NASA Astrophysics Data System (ADS)

    Bizoń, Piotr; Kahl, Michał

    2016-09-01

    We consider a spherically symmetric (magnetic) SU(2) Yang-Mills field propagating on the exterior of the extremal Reissner-Nordström black hole. Taking advantage of the conformal symmetry, we reduce the problem to the study of the Yang-Mills equation in a geodesically complete spacetime with two asymptotically flat ends. We prove the existence of infinitely many static solutions (two of which are found in closed form) and determine the spectrum of their linear perturbations and quasinormal modes. Finally, using the hyperboloidal approach to the initial value problem, we describe the process of relaxation to the static endstates of evolution, both stable (for generic initial data) and unstable (for codimension-one initial data).

  3. Quantum cosmological Friedman models with a Yang-Mills field and positive energy levels

    NASA Astrophysics Data System (ADS)

    Gerhardt, Claus

    2010-02-01

    We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a Yang-Mills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to {\\bb R}^{3} . The energy levels of the resulting quantum model, i.e. the eigenvalues of the corresponding self-adjoint Hamiltonian with a pure point spectrum, are strictly positive. This work has been supported by the DFG.

  4. Hamiltonian Formulation of the Yang-Mills field on the null-plane

    NASA Astrophysics Data System (ADS)

    Casana, R.; Pimentel, B. M.; Zambrano, G. E. R.

    2010-02-01

    We have studied the null-plane hamiltonian structure of the free Yang-Mills fields. Following the Dirac's procedure for constrained systems we have performed a detailed analysis of the constraint structure of the model and we give the generalized Dirac brackets for the physical variables. Using the correspondence principle in the Dirac's brackets we obtain the same commutators present in the literature and new ones.

  5. Bogomol'nyi equations and solutions for Einstein-Yang-Mills-dilaton-σ models

    NASA Astrophysics Data System (ADS)

    Braden, H. W.; Varela, V.

    1998-12-01

    We derive Bogomol'nyi equations for an Einstein-Yang-Mills-dilaton-σ model on a static spacetime, showing that the Einstein equations are satisfied if and only if the associated (conformally scaled) three-metric is flat. These are precisely the static metrics for which super-covariantly constant spinors exist. We study some general properties of these equations and then consider the problem of obtaining axially symmetric solutions for the gauge group SU(2).

  6. Implications of general covariance and maximum four-dimensional Yang-Mills gauge symmetry. [gravitational interactions

    NASA Technical Reports Server (NTRS)

    Hsu, J. P.

    1979-01-01

    General covariance and maximum four-dimensional Yang-Mills gauge symmetry lead to these results: (1) gravity is characterized by a dimensionless constant F of the order of 10 to the -19th; (2) the Newtonian force is always attractive; (3) space-time has a torsion; and (4) gravitational spin-force between two protons is about 10 to the 19th times stronger than the corresponding Newtonian force. A possible experimental test is discussed.

  7. An instability of hyperbolic space under the Yang-Mills flow

    SciTech Connect

    Gegenberg, Jack; Day, Andrew C.; Liu, Haitao; Seahra, Sanjeev S.

    2014-04-15

    We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence of the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.

  8. Azimuthal anisotropies in p + Pb collisions from classical Yang-Mills dynamics

    NASA Astrophysics Data System (ADS)

    Schenke, Björn; Schlichting, Sören; Venugopalan, Raju

    2015-07-01

    We compute single and double inclusive gluon distributions in classical Yang-Mills simulations of proton-lead collisions and extract the associated transverse momentum dependent Fourier harmonics v2 (pT) and v3 (pT). Gluons have a large v2 in the initial state, while odd harmonics such as v3 vanish identically at the initial time τ =0+. By the time τ ≲ 0.4 fm /c final state effects in the classical Yang-Mills evolution generate a non-zero v3 and only mildly modify the gluon v2. Unlike hydrodynamic flow, these momentum space anisotropies are uncorrelated with the global spatial anisotropy of the collision. A principal ingredient for the generation of v2 and v3 in this framework is the event-by-event breaking of rotational invariance in domains the size of the inverse of the saturation scale Qs. In contrast to our findings in p + Pb collisions Yang-Mills simulations of lead-lead collisions generate much smaller values of v2,3 (pT) and additional collective flow effects are needed to explain experimental data. This is because the locally generated anisotropy due to the breaking of rotational invariance is depleted with the increase in the number of uncorrelated domains.

  9. Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

    NASA Astrophysics Data System (ADS)

    Bouguerra, Yacine; Maamache, Mustapha; Ryeol Choi, Jeong

    2017-06-01

    Hannay’s angle is a classical analogue of the “geometrical phase factor” found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay’s angle is derived from a rigorous evaluation. The obtained Hannay’s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay’s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation, and its physical nature is addressed. Hannay’s angle, together with its quantum counterpart Berry’s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation. Supported by Basic Science Research Program through National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)

  10. Quark confinement, new cosmic expansion and general Yang-Mills symmetry

    NASA Astrophysics Data System (ADS)

    Hsu, Jong-Ping

    2017-01-01

    We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general (SU 3)color×(U 1)baryon symmetry. The phase functions in the usual gauge transformations are generalized to new ‘action integrals’. The general Yang-Mills transformations have group properties and reduce to usual gauge transformations in special cases. Both quarks and ‘gauge bosons’ are permanently confined by linear potentials. In this unified model of particle-cosmology, physics in the largest cosmos and that in the smallest quark system appear to both be dictated by the general Yang-Mills symmetry and characterized by a universal length. The basic force between two baryons is independent of distance. However, the cosmic repulsive force exerted on a baryonic supernova by a uniform sphere of galaxies is proportional to the distance from the center of the sphere. The new general Yang-Mills field may give a field-theoretic explanation of the accelerated cosmic expansion. The prediction could be tested experimentally by measuring the frequency shifts of supernovae at different distances. Supported in part by the Jingshin Resealch Fund of the UMassD Foundation

  11. Equivariant dimensional reduction and quiver gauge theories

    NASA Astrophysics Data System (ADS)

    Dolan, Brian P.; Szabo, Richard J.

    2011-09-01

    We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions.

  12. Yang-Mills like instantons in eight and seven dimensions

    NASA Astrophysics Data System (ADS)

    Loginov, E. K.; Loginova, E. D.

    2014-10-01

    We consider a gauge theory in which a nonassociative Moufang loop takes the place of a structure group. We construct Belavin-Polyakov-Schwartz-Tyupkin (BPST) and t'Hooft like instanton solutions of the gauge theory in seven and eight dimensions.

  13. Fast Galerkin BEM for 3D Potential Theory

    SciTech Connect

    Nintcheu Fata, Sylvain

    2008-01-01

    This paper is concerned with the development of a fast spectral method for solving direct and indirect boundary integral equations in 3D-potential theory. Based on a Galerkin approximation and the Fast Fourier Transform, the proposed method is a generalization of the precorrected-FFT technique to handle not only single-layer potentials but also double-layer potentials and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are presented to illustrate the performance of the method.

  14. 3D weak lensing: Modified theories of gravity

    NASA Astrophysics Data System (ADS)

    Pratten, Geraint; Munshi, Dipak; Valageas, Patrick; Brax, Philippe

    2016-05-01

    Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large-scale structure as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity. Employing a 3D analysis based on the spherical Fourier-Bessel expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution σɛ of source galaxies. Here, we focus on two classes of screened theories of gravity: (i) f (R ) chameleon models and (ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of the matter power spectrum with redshift in these theories. Using a χ2 analysis, we show that for an all-sky spectroscopic survey, the parameter fR0 can be constrained in the range fR0<5 ×10-6(9 ×10-6) for n =1 (2 ) with a 3 σ confidence level. This can be achieved by using relatively low-order angular harmonics ℓ<100 . Higher-order harmonics ℓ>100 could provide tighter constraints but are subject to nonlinear effects, such as baryonic feedback, that must be accounted for. We also employ a Principal Component Analysis in order to study the parameter degeneracies in the MG parameters. The confusion from intrinsic ellipticity correlation and modification of the matter power spectrum at a small scale due to feedback mechanisms is briefly discussed.

  15. From 4d Yang-Mills to 2d ℂℙN - 1 model: IR problem and confinement at weak coupling

    NASA Astrophysics Data System (ADS)

    Yamazaki, Masahito; Yonekura, Kazuya

    2017-07-01

    We study four-dimensional SU( N) Yang-Mills theory on R× T^3=R× {S}_A^1× {S}_B^1× {S}_C^1 , with a twisted boundary condition by a ℤ N center symmetry imposed on S B 1 × S C 1 . This setup has no IR zero modes and hence is free from IR divergences which could spoil trans-series expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T^2={S}_A× {S}_B , to connect the model to the two-dimensional ℂℙ N- 1-model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the ℤ N global symmetry of ℂℙ N- 1. There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

  16. The soft-collinear bootstrap: mathcal{N} = {4} Yang-Mills amplitudes at six- and seven-loops

    NASA Astrophysics Data System (ADS)

    Bourjaily, J. L.; DiRe, A.; Shaikh, A.; Spradlin, M.; Volovich, A.

    2012-03-01

    Infrared divergences in scattering amplitudes arise when a loop momentum ℓ becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in mathcal{N} = {4} super-Yang-Mills theory enjoy softer than expected behavior as ℓ ∥ p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively. PDF and Mathematica files with all of our results are provided at http://goo.gl/qIKe8 .

  17. Spinning superstrings at two loops: Strong-coupling corrections to dimensions of large-twist super Yang-Mills operators

    SciTech Connect

    Roiban, R.; Tseytlin, A. A.

    2008-03-15

    We consider folded (S,J) spinning strings in AdS{sub 5}xS{sup 5} (with one spin component in AdS{sub 5} and a one in S{sup 5}) corresponding to the Tr(D{sup S}{phi}{sup J}) operators in the sl(2) sector of the N=4 super Yang-Mills theory in the special scaling limit in which both the string mass {approx}{radical}({lambda})lnS and J are sent to infinity with their ratio fixed. Expanding in the parameter l=(J/{radical}({lambda})lnS) we compute the 2-loop string sigma-model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena [J. High Energy Phys. 11 (2007) 019]. We suggest that a resummation of the logarithmic l{sup 2}ln{sup n}l terms is necessary in order to establish an interpolation to the weakly coupled gauge-theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multispin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite 'renormalization' of the relation between the parameters of the classical solution and the fixed spins, i.e., the charges of the SO(2,4)xSO(6) symmetry.

  18. Vacuum structure and string tension in Yang-Mills dimeron ensembles

    NASA Astrophysics Data System (ADS)

    Zimmermann, Falk; Forkel, Hilmar; Müller-Preußker, Michael

    2012-11-01

    We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties as a function of the bare coupling. In particular, we examine the extent to which these ensembles and their classical gauge interactions capture topological and confinement properties of the Yang-Mills vacuum. This also allows us to put the classic picture of meron-induced quark confinement, with the confinement-deconfinement transition triggered by dimeron dissociation, to stringent tests. In the first part of our analysis we study spacial, topological-charge and color correlations at the level of both the dimerons and their meron constituents. At small to moderate couplings, the dependence of the interactions between the dimerons on their relative color orientations is found to generate a strong attraction (repulsion) between nearest neighbors of opposite (equal) topological charge. Hence, the emerging short- to mid-range order in the gauge-field configurations screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their less localized meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to the long-range tails of these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, “instantonlike” dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence, the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a

  19. Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario

    NASA Astrophysics Data System (ADS)

    Casana, R.; Ferreira, M. M.; da Hora, E.; dos Santos, C.

    2013-05-01

    We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in R. Casana et al. (2012) [1]. Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and usual finite energy boundary conditions. Moreover, the new solutions are classified in two different types according to their capability of recovering (or not) the usual 't Hooft-Polyakov monopole. Finally, we compare the profiles of the solutions we found with the standard ones, from which we comment about the main features exhibited by the new configurations.

  20. On hydrogen-like bound states in N = 4 super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Sakata, Yusuke; Schneider, Robin; Tachikawa, Yuji; Yamaura, Takemasa

    2017-09-01

    Using relativistic quantum mechanics, we study the spectrum of a non-BPS two-particle bound state in the massive phase of N = 4 super Yang-Mills, in the limit when one of the particles is infinitely heavier than the other. We find that the spectrum shows the exact n 2 degeneracy for each principal quantum number n, just as in the strict non-relativistic limit. This is in line with the findings of Caron-Huot and Henn, who studied the same system in the large N limit with the technique of integrability and the dual conformal symmetry.

  1. Evolution of the Magnetic Component in Yang-Mills Condensate Dark Energy Models

    NASA Astrophysics Data System (ADS)

    Zhao, Wen; Xu, Donghui

    The evolution of the electric and magnetic components in an effective Yang-Mills condensate dark energy model is investigated. If the electric field is dominant, the magnetic component disappears with the expansion of the Universe. The total YM condensate tracks the radiation in the earlier Universe, and later it becomes wy ~ -1 and is thus similar to the cosmological constant. So the cosmic coincidence problem can be avoided in this model. However, if the magnetic field is dominant, wy > 1/3 holds for all time, suggesting that it cannot be a candidate for the dark energy in this case.

  2. K-decompositions and 3d gauge theories

    SciTech Connect

    Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

    2016-11-24

    This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space $\\mathcal{L}$K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $\\mathcal{L}$K(M) as a Lagrangian subvariety in the symplectic moduli space XunK(∂M) of framed flat connections on the boundary — and more so, as a “K2-Lagrangian,” meaning that the K2-avatar of the symplectic form restricts to zero. We construct an open part of $\\mathcal{L}$K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $\\mathcal{L}$K(M) is K2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $\\mathcal{L}$K(M) is K2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories TK [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories TK [M] are described as IR fixed points of abelian Chern-Simons-matter theories

  3. K-decompositions and 3d gauge theories

    DOE PAGES

    Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

    2016-11-24

    This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli spacemore » $$\\mathcal{L}$$K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $$\\mathcal{L}$$K(M) as a Lagrangian subvariety in the symplectic moduli space XunK(∂M) of framed flat connections on the boundary — and more so, as a “K2-Lagrangian,” meaning that the K2-avatar of the symplectic form restricts to zero. We construct an open part of $$\\mathcal{L}$$K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $$\\mathcal{L}$$K(M) is K2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $$\\mathcal{L}$$K(M) is K2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories TK [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories TK [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between Nf = 1 SQED

  4. The coupling of gravity to Yang-Mills fields and fermions in static, spherically symmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Bernard, Yann L.-H.

    The goal of this dissertation is to provide a systematic treatment of the coupling of fermions to non-Abelian Yang-Mills fields with gauge groups SU(N) in a static and spherically symmetric four-dimensional Lorentzian spacetime. We begin by reviewing the basic mathematical foundations and physical notions required to develop the appropriate models describing the coupled configuration. We shall present a new way to produce a consistent ansatz for the Yang-Mills potential when quantum effects are taken into account. We show that this new constructive algorithm yields a potential with the same structure as its classical counterpart commonly found in the literature. With the help of our ansatz, we derive the full coupled systems of ordinary differential equations for an electromagnetic potential with gauge group SU(N). Various results rendering account of the differences and the similarities there exist between the case when N is even and the case when N is odd are exposed in great details. Finally, an in-depth analysis of the electromagnetic coupled equations is presented, when N is an even natural number. We demonstrate, in particular, that under relatively weak hypotheses on the metric, such coupling admits no globally normalizable black-hole solutions, thereby substantially extending two theorems of Finster, Smoller and Yau.

  5. Spherically symmetric solutions of a (4 + n)-dimensional Einstein Yang Mills model with cosmological constant

    NASA Astrophysics Data System (ADS)

    Brihaye, Yves; Hartmann, Betti

    2005-01-01

    We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.

  6. Self-dual MacDowell-Mansouri gravity coupled to self-dual Yang-Mills fields

    NASA Astrophysics Data System (ADS)

    Chee, G. Y.

    2000-09-01

    A unified action for self-dual MacDowell-Mansouri gravity and Yang-Mills fields is proposed. The dual operation acting on the curvature and the self-dual and anti-self-dual decomposition are performed with respect to spacetime indices rather than internal indices, which makes the action simpler than the one given by Nieto and Socorro. In the new action the (anti-)self-dual Yang-Mills curvature couples only to the (anti-)self-dual curvature of the spacetime and then the self-dual and the anti-self-dual parts of the action are separated completely.

  7. Some exact solutions of (2+1)-dimensional Yang-Mills equations with the Chern-Simons term

    SciTech Connect

    Oh, C. H.; Sia, L. C.; Teh, R.

    1989-07-15

    Two /ital Ansa/$/ital uml/---/ital tze/ for the gauge field potential are given so that the(2+1)-dimensional Yang-Mills equations with the Chern-Simons termcan be solved in terms of the modified Bessel functions and the ellipticfunction respectively.

  8. The 3-D lattice theory of Flower Constellations

    NASA Astrophysics Data System (ADS)

    Davis, Jeremy J.; Avendaño, Martín E.; Mortari, Daniele

    2013-08-01

    Flower Constellations (FCs) have been extensively studied for use in optimal constellation design. The Harmonic FCs (HFCs) subset, representing the symmetric configurations, have recently been reformulated into 2-D Lattice Flower Constellations (2D-LFCs), encompassing the complete set of HFCs. Elliptic orbits are generally avoided due to the deleterious effects of Earth's oblateness on the constellation, but here we present a novel concept for avoiding this problem and enabling more effective global coverage utilizing elliptic orbits. This new 3D Lattice Flower Constellations (3D-LFCs) framework generalizes the 2D-LFCs, Walker constellations, elliptical Walker constellations, and many of Draim's global coverage constellations. Previous studies have shown FCs can provide improved performance in global navigation over existing Global Navigation Satellite Systems (GNSS). We found a 3D-LFC design that improved the average positioning accuracy by 3.5 % while reducing launch \\varDelta v requirements when compared to the existing Galileo GNSS constellation.

  9. Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

    NASA Astrophysics Data System (ADS)

    Kassandrov, Vladimir V.; Rizcallah, Joseph A.

    We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

  10. Anisotropic N=4 Super-Yang-Mills Plasma and Its Instabilities

    SciTech Connect

    Mateos, David; Trancanelli, Diego

    2011-09-02

    We present a type-IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super-Yang-Mills plasma. The solution is static and completely regular. The full geometry can be viewed as a renormalization group flow from an ultraviolet anti-de Sitter geometry to an infrared Lifshitz-like geometry. The anisotropy can be equivalently understood as resulting from a position-dependent {theta} term or from a nonzero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e., mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

  11. Statefinder Parameters for the Quantum Effective Yang-Mills Condensate Dark Energy Model

    NASA Astrophysics Data System (ADS)

    Tong, Minglei; Zhang, Yang; Xia, Tianyang

    The quantum effective Yang-Mills condensate (YMC) dark energy model has some distinctive features so that it naturally solves the coincidence problem and, at the same time, is able to give an equation of state w crossing -1. In this work we further employ the statefinder pair (r,s), introduced by Sahni et al., to diagnose the YMC model for three cases: the noncoupling, the YMC decaying into matter only, and the YMC decaying into both matter and radiation. The trajectories (r,s) and (r,q), and the evolutions r(z) and s(z), are explicitly presented. It is found that the YMC model in all three cases has r ≃ 1 for z < 10 and s ≃ 0 for z < 5 with only small deviations, ≃ 0.02, quite close to the cosmological constant model (LCDM), but is obviously differentiated from other dark energy models, such as quiessence or kinessence.

  12. Bonus symmetry and the operator product expansion of N = 4 super-Yang-Mills

    NASA Astrophysics Data System (ADS)

    Intriligator, Kenneth; Skiba, Witold

    1999-10-01

    The superconformal group of N = 4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus U(1) y R-symmetry, which acts as an automorphism of the superconformal group. This conjecture is for arbitrary gauge group G and gauge coupling gYM. A consequence is that n ⩽ 4-point functions involving only short operators exactly respect the U(1) Y symmetry, as has been previously conjectured based on AdS duality. This, in turn, would imply that all n ⩽ 3-point functions involving only short operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are compatible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2, Z) modular transformation properties are discussed.

  13. Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography

    NASA Astrophysics Data System (ADS)

    Banks, Elliot

    2016-07-01

    Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and U(1) gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these U(1) charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.

  14. Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

    NASA Astrophysics Data System (ADS)

    Rinaldi, Massimiliano

    2015-10-01

    We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

  15. Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime

    NASA Astrophysics Data System (ADS)

    Bizoń, Piotr; Rostworowski, Andrzej; Zenginoǧlu, Anıl

    2010-09-01

    We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills field propagating outside the Schwarzschild black hole. Although solutions starting from smooth finite energy initial data remain smooth for all times, not all of them scatter since there are non-generic solutions which asymptotically tend towards unstable static solutions. We show that a static solution with one unstable mode appears as an intermediate attractor in the evolution of initial data near a border between basins of attraction of two different vacuum states. We study the saddle-point dynamics near this attractor; in particular, we identify the universal phases of evolution: the ringdown approach, the exponential departure and the eventual decay to one of the vacuum states.

  16. Quantum phases of Yang-Mills matrix model coupled to fundamental fermions

    NASA Astrophysics Data System (ADS)

    Pandey, Mahul; Vaidya, Sachindeo

    2017-02-01

    By investigating the SU(2) Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. As a consequence of our analysis, we show that 2-color quantum chromodynamics coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase.

  17. SL(2,R) matrix model and supersymmetric Yang-Mills integrals

    SciTech Connect

    Tierz, Miguel

    2007-11-15

    The density of states of Yang-Mills integrals in the supersymmetric case is characterized by power-law tails whose decay is independent of N, the rank of the gauge group. It is believed that this has no counterpart in matrix models, but we construct a matrix model that exactly exhibits this property. In addition, we show that the eigenfunctions employed to construct the matrix model are invariant under the collinear subgroup of conformal transformations, SL(2,R). We also show that the matrix model itself is invariant under a fractional linear transformation. The wave functions of the model appear in the trigonometric Rosen-Morse potential and in free relativistic motion on anti-de Sitter space.

  18. A new phase for the anisotropic N=4 super Yang-Mills plasma

    NASA Astrophysics Data System (ADS)

    Banks, Elliot; Gauntlett, Jerome P.

    2015-09-01

    Black hole solutions of type IIB supergravity have been previously constructed that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. The zero temperature limit of these black holes approach a Lifshitz-like scaling solution in the infrared. We show that these black holes become unstable at low temperature and we construct a new class of black hole solutions which are thermodynamically preferred. The phase transition is third order and incorporates a spontaneous breaking of the SO(6) global symmetry down to SO(4) × SO(2). The critical exponents for the phase transition are given by ( α, β, γ, δ) = (-1, 1, 1, 2) which differ from the standard mean-field exponents usually seen in holography. At low temperatures the black holes approach a novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation. We show that the new ground states are thermal insulators in the direction of the anisotropy.

  19. Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

    SciTech Connect

    Rinaldi, Massimiliano

    2015-10-01

    We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

  20. Exact solutions of (n+1)-dimensional Yang-Mills equations in curved space-time

    SciTech Connect

    Sanchez-Monroy, J.A.; Quimbay, C.J.

    2012-09-15

    In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time, for the cases n=1,2,3. As an application of the results obtained for the case n=3, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case n=2 is a description of the (2+1) electrodynamics in the presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case n=1 is invariant under a parity transformation and has the form of a linear confining solution. - Highlights: Black-Right-Pointing-Pointer We study exact static confining solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time. Black-Right-Pointing-Pointer The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background. Black-Right-Pointing-Pointer A expression for the confinement potential in low dimensionality is found.

  1. Propagation properties and condensate formation of the confined Yang-Mills field

    NASA Astrophysics Data System (ADS)

    Stingl, M.

    1986-12-01

    The dynamical generation of a pole in the self-energy of a Yang-Mills field-an extension of the Schwinger mechanism-establishes a link between the tendency of the field to form nonperturbative vacuum condensates and its ``noninterpolating'' property in the confining phase-the fact that it has no particles associated with it. The nonvanishing residue of such a pole-a parameter b4 of dimension (mass)4-on the one hand provides for a nonvanishing value of <0||(∂μAν-∂νAμ)2 ||0>, a contribution to the ``gluon condensate.'' On the other hand, it implies a dominant nonperturbative form of the propagator that has no particle singularity on the real k2 axis; instead, it describes a quantized field whose elementary excitations are short lived. The dispersion law for these excitations is given and shows that they grow more particlelike (are asymptotically free) at large momenta, thus providing a qualitative description of the short-lived excitation at the origin of a gluon jet. At large k2, the nonperturbative propagator reproduces nonperturbative corrections derived from the operator-product expansion. Moreover, it is a solution to the Euclidean Dyson-Schwinger equation for the Yang-Mills field in the following sense: there exist nonperturbative three-vector vertices Γ3 and auxiliary ghost-ghost-vector vertices G3, satisfying all symmetry and invariance requirements, and in conjunction with which this propagator solves both the Euclidean Dyson-Schwinger equation through one-dressed-loop terms and the Γ3 Slavnov-Taylor identity up to perturbative corrections of order g2. The consistency conditions for this solution give b2=μ0 2exp[-(4π)2 /11g2] to this order, confirming the nonperturbative nature of the residue parameter, and providing a paradigm for the dynamical determination of condensates.

  2. MOM3D method of moments code theory manual

    NASA Technical Reports Server (NTRS)

    Shaeffer, John F.

    1992-01-01

    MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

  3. K-decompositions and 3d gauge theories

    NASA Astrophysics Data System (ADS)

    Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

    2016-11-01

    This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL( K, ℂ)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space ℒ K ( M) of framed flat connections on the boundary ∂ M that extend to M. Our goal is to understand an open part of ℒ K ( M) as a Lagrangian subvariety in the symplectic moduli space {{X}}_K^{un}(partial M) of framed flat connections on the boundary — and more so, as a "K2-Lagrangian," meaning that the K2-avatar of the symplectic form restricts to zero. We construct an open part of ℒ K ( M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston's gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL( K, ℂ)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of ℒ K ( M) is K2-isotropic as long as ∂ M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that ℒ K ( M) is K2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K2-Lagrangian property to a combinatorial statement.

  4. Non-existence of black-hole solutions for the electroweak Einstein Dirac Yang/Mills equations

    NASA Astrophysics Data System (ADS)

    Bernard, Yann

    2006-07-01

    We consider a static, spherically symmetric system of a Dirac particle interacting with classical gravity and an electroweak Yang Mills field. It is shown that the only black-hole solutions of the corresponding coupled equations must be the extreme Reissner Nordström solutions, locally near the event horizon. This work generalizes a series of papers published by F Finster, J Smoller and S-T Yau.

  5. Black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions

    NASA Astrophysics Data System (ADS)

    Meng, K.; Li, J.

    2016-10-01

    We construct a new static black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions. We calculate the thermodynamical quantities of the black hole and check the first law of black hole thermodynamics. Thermal stability of the black hole is explored in the context of both canonical and grand canonical ensembles. By identifying the cosmological constant as the pressure of the gravitational system, we study the phase transitions of the black hole.

  6. The three-loop Yang-Mills condensate dark energy model and its cosmological constraints

    NASA Astrophysics Data System (ADS)

    Wang, S.; Zhang, Y.; Xia, T. Y.

    2008-10-01

    This work is a comprehensive investigation of the Yang-Mills condensate (YMC) dark energy (DE) model, which is extended to include the three-loop quantum corrections. We study its cosmic evolution and the possibility of crossing the phantom divide w = -1, examine in detail the Hubble parameter H, the deceleration parameter q, the statefinder (r,s) diagnostic and the w-w' diagnostic for the model without and with interaction, and compare our results with other DE models. Also, using the observational data for type Ia supernovae (SNIa), the shift parameter from the cosmic microwave background (CMB), and the baryon acoustic oscillation peak from large scale structures (LSS), we give the cosmological constraints on the three-loop YMC model. It is found that the model can solve the coincidence problem naturally, and its prediction of the aforementioned parameter is much closer to the ΛCDM (CDM: cold dark matter) model one than those from other dynamical DE models; the introduction of the matter-DE interaction will make the YMC model deviate from the ΛCDM model, and will give an equation of state crossing -1. Moreover, it is also found that, for fitting the latest SNIa data alone, the ΛCDM model is slightly better than the three-loop YMC model; but in fitting the combination of SNIa, CMB and LSS data, the three-loop YMC model performs better than the ΛCDM model.

  7. Confinement of quarks and valence gluons in SU( N) Yang-Mills-Higgs models

    NASA Astrophysics Data System (ADS)

    Oxman, L. E.

    2013-03-01

    In this work, we analyze a class of Yang-Mills models containing adjoint Higgs fields, with SU( N) symmetry spontaneously broken down to Z( N), showing they contain center vortices, Y-junctions formed by them, and junctions where different center vortices are smoothly interpolated by monopole-like configurations. In the context of dual superconductors, these objects represent different states of the gluon field. Center vortices confine quarks to form normal hadron states. The interpolating monopole, which in our model cannot exist as an isolated configuration, is identified with a confined valence gluon. A junction containing a monopole can bind quarks in a color nonsinglet state to form an overall neutral object, identified with a hybrid hadron. These states, formed by quarks bound to a valence gluon, are allowed by QCD, and current experimental collaborations are aimed at identifying them. Finally, considering the general version of the model, based on a compact simple gauge group G, the picture is completed with a heuristic discussion about why it would be natural using as G the dual of the chromoelectric gauge group G e, and external pointlike monopoles to represent the mesonic and baryonic Wilson loops.

  8. Observational constraints on a Yang-Mills condensate dark energy model

    NASA Astrophysics Data System (ADS)

    Fu, Z. W.; Zhang, Y.; Tong, M. L.

    2011-11-01

    Using the recently released Union2 compilation with 557 Type Ia supernovae, the shift parameter of the cosmic microwave background given by the WMAP7 observations and the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey, we perform the χ2 analysis on the 1-loop Yang-Mills condensate (YMC) dark energy model. The analysis has been made for both non-coupling and coupling models with Ωm0 and w0 being treated as free parameters. It is found that χ2min = 542.870 at Ωm0 = 0.2701 and w0 = -0.9945 for the non-coupling model, and χ2min = 542.790 at γ = -0.015, Ωm0 = 0.2715 and w0 = -0.9969 for the coupling model. Comparing with the ΛCDM model, the YMC model has a smaller χ2min, but it has greater values of the Bayesian and Akaike information criteria. Overall, YMC is as robust as ΛCDM.

  9. D3-D5 theories with unquenched flavors

    NASA Astrophysics Data System (ADS)

    Conde, Eduardo; Lin, Hai; Penín, José Manuel; Ramallo, Alfonso V.; Zoakos, Dimitrios

    2017-01-01

    We construct the string duals of the defect theories generated when Nf flavor D5-branes intersect Nc color D3-branes along a 2 + 1 dimensional subspace. We work in the Veneziano limit in which Nc and Nf are large and Nf /Nc is fixed. By smearing the D5-branes, we find supergravity solutions that take into account the backreaction of the flavor branes and preserve two supercharges. When the flavors are massless the resulting metric displays an anisotropic Lifshitz-like scale invariance. The case of massive quarks is also considered.

  10. SU (2) Dirac-Yang-Mills quantum mechanics of spatially constant quark and gluon fields

    NASA Astrophysics Data System (ADS)

    Pavel, H.-P.

    2011-06-01

    The quantum mechanics of spatially constant SU (2) Yang-Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields, which Abelianises the Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. In the same way as this reduces the colored spin-1 gluons to unconstrained colorless spin-0 and spin-2 gluons, it reduces the colored spin-1/2 quarks to unconstrained colorless spin-0 and spin-1 quarks. These however continue to satisfy anti-commutation relations and hence the Pauli-exclusion principle. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. In this form the low-energy spectrum can be obtained with high accuracy. As an illustrative example, the spin-0 energy-spectrum of the quark-gluon system is calculated for massless quarks of one flavor. It is found, that only for the case of 4 reduced quarks (half-filling) satisfying the boundary condition of particle-antiparticle C-symmetry, states with energy lower than for the pure-gluon case are obtained. These are the ground state, with an energy about 20% lower than for the pure-gluon case and the formation of a quark condensate, and the sigma-antisigma excitation with an energy about a fifth of that of the first glueball excitation.

  11. ahcal{N} = 4 super-Yang-Mills in LHC superspace part II: non-chiral correlation functions of the stress-tensor multiplet

    NASA Astrophysics Data System (ADS)

    Chicherin, Dmitry; Sokatchev, Emery

    2017-03-01

    We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N = 4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.

  12. Strolling along gauge theory vacua

    NASA Astrophysics Data System (ADS)

    Seraj, Ali; Van den Bleeken, Dieter

    2017-08-01

    We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.

  13. Spin-connection generalized Yang--Mills fields on double-dual generalized Einstein--Cartan backgrounds

    SciTech Connect

    O'Brien, G.M.; Tchrakian, D.H.

    1988-05-01

    In every even dimension, a modification of the generalized Yang--Mills systems (modGYM) is introduced. It is shown that spin-connection modGYM fields, which are self-dual on a double-self-dual background of generalized Einstein--Cartan (GEC) gravity, can be constructed: this generalizes the constructions of Charap and Duff (Phys. Lett. B 69, 445 (1977)) in four dimensions, to all even dimensions. Additional duality constraints are also given that must be satisfied by the gravitational fields, if these constructions are to apply also to the full GYM systems. Applications to compactification, as well as relevant physical criteria, are briefly discussed.

  14. Spin-connection generalized Yang-Mills fields on double-dual generalized Einstein-Cartan backgrounds

    NASA Astrophysics Data System (ADS)

    O'Brien, G. M.; Tchrakian, D. H.

    1988-05-01

    In every even dimension, a modification of the generalized Yang-Mills systems (modGYM) is introduced. It is shown that spin-connection modGYM fields, which are self-dual on a double-self-dual background of generalized Einstein-Cartan (GEC) gravity, can be constructed—this generalizes the constructions of Charap and Duff [Phys. Lett. B 69, 445 (1977)] in four dimensions, to all even dimensions. Additional duality constraints are also given that must be satisfied by the gravitational fields, if these constructions are to apply also to the full GYM systems. Applications to compactification, as well as relevant physical criteria, are briefly discussed.

  15. Nonsupersymmetric strong coupling background from the large N quantum mechanics of two matrices coupled via a Yang-Mills interaction

    SciTech Connect

    Rodrigues, Joao P.; Zaidi, Alia

    2010-10-15

    We derive a planar sector of the large N nonsupersymmetric background of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction, in terms of the density of eigenvalues of one of the matrices. This background satisfies an implicit nonlinear integral equation, with a perturbative small coupling expansion and a solvable large coupling solution, which is obtained. The energy of system and the expectation value of several correlators are obtained in this strong coupling limit. They are free of infrared divergences.

  16. Exploring center strings in S U (2 ) and S U (3 ) relativistic Yang-Mills-Higgs models

    NASA Astrophysics Data System (ADS)

    Oxman, L. E.; Vercauteren, D.

    2017-01-01

    We develop numerical tools and apply them to solve the relativistic Yang-Mills-Higgs equations in a model where the S U (N ) symmetry is spontaneously broken to its center. In S U (2 ) and S U (3 ), we obtain the different field profiles for infinite and finite center strings, with end points at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of S U (2 ) fields leads us to a reference point where an Abelian-like Bogomol'nyi-Prasad-Sommereld (BPS) bound is reconciled with N -ality.

  17. Some initial theory and practice exploration for 3D digital sea-route

    NASA Astrophysics Data System (ADS)

    Sui, Haigang; Zhang, Anmin; Wang, Juan; Hua, Li

    2005-10-01

    The safe navigation of Yangtse River is one of important system engineering. Traditional 2D electronic river map is very effective to ensure safe navigation. However, it is not visual and many kinds of complex analysis are difficult in 2D environment and they only can be processed in 3D situation. So the 3D digital sea-route is very important and urgent to realize digital and intelligent safe navigation. Aiming at this, a whole framework for 3D digital sea-route is first introduced. Under this framework, integrated services from sea-route data colleting, data storing, data management, data processing, data query and analysis, to data distribution and application are illustrated. And some key theory and techniques including automatic sounding creation and processing techniques, the sea-route 3D model production art based on GIS & CAD, the organization and management techniques of multi-source, multi-type, multi-scale data, the 3D dynamic visualization techniques for huge data, the 2D & 3D mutually display and analysis techniques are discussed in detail. Based on these theory and techniques, a system named TEAVIS for 3D digital sea-route is developed. This system is applied in the Marine Safety Administration Bureau of Tianjin City and the Yangtse River Sea-route Bureau and obtained good evaluation.

  18. Renormalization of composite operators in Yang-Mills theories using a general covariant gauge

    SciTech Connect

    Collins, J.C.; Scalise, R.J. )

    1994-09-15

    Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear when gluonic matrix elements are taken on shell at zero momentum transfer.

  19. The Gribov problem in presence of background field for SU(2) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Canfora, Fabrizio; Hidalgo, Diego; Pais, Pablo

    2016-12-01

    The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.

  20. Infrared suppression of the Coulomb gauge gluon propagator in SU(3) Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Nakagawa, Y.

    We calculate the equal-time transverse gluon propagator in Coulomb gauge QCD using a SU(3) quenched lattice gauge simulation on large lattices, up to 114 [fm4 ]. We find that the equal-time gluon propagator shows scaling violation; namely, the data for different lattice spacings do not fall on top of one curve. This problem is cured by discarding data at large momenta, which suffer from discretization errors. In the infrared region, the transverse gluon propagator is strongly suppressed and shows a turnover at about 500 [MeV]. Fitting the power law ansatz to the data at small momenta predicts the vanishing gluon propagator at zero momentum, indicating the confinement of gluons.

  1. Dual Meissner Effect and Non-Abelian Magnetic Monopole in SU(3) Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru

    2013-03-01

    We measure the color flux produced by a pair of quark and antiquark and examine whether or not the non-Abelian dual superconductivity claimed by us is indeed a mechanism of quark confinement. We present a preliminary result of the direct evidence for the non-abelian dual Meissner effect, that is to say, restricted U(2)-field part of the flux tube plays the dominant role in the quarkantiquark potential.

  2. Three-point vertex functions in Yang-Mills Theory and QCD in Landau gauge

    NASA Astrophysics Data System (ADS)

    Blum, Adrian L.; Alkofer, Reinhard; Huber, Markus Q.; Windisch, Andreas

    2017-03-01

    Solutions for the three-gluon and quark-gluon vertices from Dyson-Schwinger equations and the three-particle irreducible formalism are discussed. Dynamical quarks ("unquenching") change the three-gluon vertex via the quark-triangle diagrams which themselves include fully dressed quark-gluon vertex functions. On the other hand, the quark-swordfish diagram is, at least with the model used for the two-quark-two-gluon vertex employed here, of minor importance. For the leading tensor structure of the threegluon vertex the "unquenching" effect can be summarized for the nonperturbative part as a shift of the related dressing function towards the infrared.

  3. Holography for field theory solitons

    NASA Astrophysics Data System (ADS)

    Domokos, Sophia K.; Royston, Andrew B.

    2017-07-01

    We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS4 × S 2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asymptotically AdS4 × S 2 spacetimes, which are invariant under eight supersymmetries. With future holographic applications in mind, we analyze the vacuum structure and perturbative spectrum of the Yang-Mills theory on AdS4 × S 2, as well as systems of BPS equations for finite-energy solitons. Finally, we demonstrate that the classical Yang-Mills theory has a consistent truncation on the two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS4.

  4. Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory

    DOE PAGES

    Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; ...

    2016-10-20

    We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studyingmore » two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.« less

  5. Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory

    SciTech Connect

    Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin

    2016-10-20

    We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

  6. Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory

    NASA Astrophysics Data System (ADS)

    Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin

    2016-10-01

    We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N=4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality — an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

  7. Energy loss of a nonaccelerating quark moving through a strongly coupled N =4 super Yang-Mills vacuum or plasma in strong magnetic field

    NASA Astrophysics Data System (ADS)

    Mamo, Kiminad A.

    2016-08-01

    Using AdS /CFT correspondence, we find that a massless quark moving at the speed of light v =1 , in arbitrary direction, through a strongly coupled N =4 super Yang-Mills (SYM) vacuum at T =0 , in the presence of strong magnetic field B , loses its energy at a rate linearly dependent on B , i.e., d/E d t =-√{λ/} 6 π B . We also show that a heavy quark of mass M ≠0 moving at near the speed of light v2=v*2=1 -4/π2T2 B ≃1 , in arbitrary direction, through a strongly coupled N =4 SYM plasma at finite temperature T ≠0 , in the presence of strong magnetic field B ≫T2, loses its energy at a rate linearly dependent on B , i.e., d/E d t =-√{λ/}6 π B v*2≃-√{λ/}6 π B . Moreover, we argue that, in the strong magnetic field B ≫T2 (IR) regime, N =4 SYM and adjoint QCD theories (when the adjoint QCD theory has four flavors of Weyl fermions and is at its conformal IR fixed point λ =λ*) have the same microscopic degrees of freedom (i.e., gluons and lowest Landau levels of Weyl fermions) even though they have quite different microscopic degrees of freedom in the UV when we consider higher Landau levels. Therefore, in the strong magnetic field B ≫T2 (IR) regime, the thermodynamic and hydrodynamic properties of N =4 SYM and adjoint QCD plasmas, as well as the rates of energy loss of a quark moving through the plasmas, should be the same.

  8. Equations on knot polynomials and 3d/5d duality

    NASA Astrophysics Data System (ADS)

    Mironov, A.; Morozov, A.

    2012-10-01

    We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as "differential" and (quantum) ̂A-polynomial structures. We pay a special attention to identity between the ̂A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d - 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.

  9. Equations on knot polynomials and 3d/5d duality

    SciTech Connect

    Mironov, A.; Morozov, A.

    2012-09-24

    We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.

  10. IR dualities in general 3d supersymmetric SU( N) QCD theories

    NASA Astrophysics Data System (ADS)

    Aharony, Ofer; Fleischer, Daniel

    2015-02-01

    In the last twenty years, low-energy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four space-time dimensions and in three space-time dimensions. In particular, duals have been found for 3d = 2 supersymmetric QCD theories with gauge group U( N), with chiral multiplets in the fundamental representation, with F chiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, and k for which the theory preserves supersymmetry. For SU( N) theories the duals have been found in some cases, such as F = and =0, but not in the general case. In this note we find the IR dual for SU( N) SQCD theories with general values of N, F, and k ≠ 0 which preserve supersymmetry.

  11. The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable

    NASA Astrophysics Data System (ADS)

    Bochicchio, Marco

    2017-03-01

    Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

  12. The cognitive apprenticeship theory for the teaching of mathematics in an online 3D virtual environment

    NASA Astrophysics Data System (ADS)

    Bouta, Hara; Paraskeva, Fotini

    2013-03-01

    Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective. To this end, we propose a pedagogical framework based on the cognitive apprenticeship for deriving principles and guidelines to inform the design, development and use of a 3D virtual environment. This study examines how the use of a 3D virtual world facilitates the teaching of mathematics in primary education by combining design principles and guidelines based on the Cognitive Apprenticeship Theory and the teaching methods that this theory introduces. We focus specifically on 5th and 6th grade students' engagement (behavioral, affective and cognitive) while learning fractional concepts over a period of two class sessions. Quantitative and qualitative analyses indicate considerable improvement in the engagement of the students who participated in the experiment. This paper presents the findings regarding students' cognitive engagement in the process of comprehending basic fractional concepts - notoriously hard for students to master. The findings are encouraging and suggestions are made for further research.

  13. Twisted 3D N=4 supersymmetric YM on deformed A{sub 3}{sup *} lattice

    SciTech Connect

    Saidi, El Hassan

    2014-01-15

    We study a class of twisted 3D N=4 supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice L{sub 3D} formally denoted as L{sub 3D}{sup su{sub 3}×u{sub 1}} and given by non-trivial fibration L{sub 1D}{sup u{sub 1}}×L{sub 2D}{sup su{sub 3}} with base L{sub 2D}{sup su{sub 3}}=A{sub 2}{sup *}, the weight lattice of SU(3). We first, develop the twisted 3D N=4 SYM in continuum by using superspace method where the scalar supercharge Q is manifestly exhibited. Then, we show how to engineer the 3D lattice L{sub 3D}{sup su{sub 3}×u{sub 1}} that host this theory. After that we build the lattice action S{sub latt} invariant under the following three points: (i) U(N) gauge invariance, (ii) BRST symmetry, (iii) the S{sub 3} point group symmetry of L{sub 3D}{sup su{sub 3}×u{sub 1}}. Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on L{sub 2D}≡L{sub 2D}{sup su{sub 2}×u{sub 1}}, the extension to twisted maximal 5D SYM with 16 supercharges on lattice L{sub 5D}≡L{sub 5D}{sup su{sub 4}×u{sub 1}} as well as the relation with known results are also given.

  14. Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory

    SciTech Connect

    Kalnins, E.G.; Kress, J.M.; Miller, W. Jr.

    2006-04-15

    This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Staeckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Staeckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.

  15. Two-phase region of vortex-solid melting: 3D XY theory

    NASA Astrophysics Data System (ADS)

    Friesen, M.; Muzikar, P.

    1998-07-01

    In clean enough samples of the high-Tc oxide materials, the phase transition into the superconducting state occurs along a first-order line in the H-T plane. This means that a two-phase region occurs in the B-T plane, in which the liquid and solid vortex phases coexist. We discuss the thermodynamics of this two-phase region, developing formulae relating experimental quantities of interest. We then apply the 3D XY scaling theory to the problem, obtaining detailed predictions for the boundaries of the coexistence region. By using published data, we are able to predict the width of the two-phase region, and determine the physical parameters involved in the 3D XY description.

  16. Transfer of learning between 2D and 3D sources during infancy: Informing theory and practice

    PubMed Central

    Barr, Rachel

    2010-01-01

    The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a 2-Dimensional (2D) representation and a 3-Dimensional (3D) object. Understanding the conditions under which young children might accomplish this particular kind of transfer is important because by 2 years of age 90% of US children are viewing television on a daily basis. Recent research shows that children can imitate actions presented on television using the corresponding real-world objects, but this same research also shows that children learn less from television than they do from live demonstrations until they are at least 3 years old; termed the video deficit effect. At present, there is no coherent theory to account for the video deficit effect; how learning is disrupted by this change in context is poorly understood. The aims of the present review are (1) to review the conditions under which children transfer learning between 2D images and 3D objects during early childhood, and (2) to integrate developmental theories of memory processing into the transfer of learning from media literature using Hayne’s (2004) developmental representational flexibility account. The review will conclude that studies on the transfer of learning between 2D and 3D sources have important theoretical implications for general developmental theories of cognitive development, and in particular the development of a flexible representational system, as well as policy implications for early education regarding the potential use and limitations of media as effective teaching tools during early childhood. PMID:20563302

  17. Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge Theory

    SciTech Connect

    Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko

    2005-06-03

    We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED{sub 3} and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.

  18. A geometric method of constructing exact solutions in modified f(R, T)-gravity with Yang-Mills and Higgs interactions

    NASA Astrophysics Data System (ADS)

    Vacaru, Sergiu I.; Veliev, Elşen Veli; Yazici, Enis

    2014-09-01

    We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.

  19. Symmetries of the 4D self-dual Yang-Mills equation and the reduction to the 2D KdV equation

    SciTech Connect

    HoSeong La )

    1992-04-01

    The Lie-point and the Lie-Baecklund symmetries of 4D self-dual Yang-Mills equation are investigated as those of differential equations. The Lie-point symmetry is nothing but the gauge symmetry at the level of field equation, but the Lie-Baecklund symmetries are new. In particular, by the symmetry reduction to KdV equation in 2D the corresponding Lie-Baecklund symmetries which reduce to the isospectral symmetries or to the nonisospectral symmetries are identified. Some speculations on the existence of the self-dual Yang-Mills hierarchy as well as the derivation of the 4D analogue of the string equation of the nonperturbative 2D quantum gravity are given.

  20. Event-by-Event Anisotropic Flow in Heavy-ion Collisions from Combined Yang-Mills and Viscous Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju

    2013-01-01

    Anisotropic flow coefficients v1-v5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated vn data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v2, v3 and v4 measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

  1. Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields

    SciTech Connect

    Doneux, J.; Saint-Aubin, Y.; Vinet, L.

    1982-01-15

    Classical solutions to the Minkowskian field equations of a Yang-Mills system coupled to an isospinor of massless Dirac fields are found. The Dirac fields are taken in the fundamental representation of SU(2). In view of the conformal and Weyl inveriance of the Lagrangian, the solutions are obtained by considering the system over the compactification M-bar of Minkowski space. M-bar is diffeomorphic to SU(2)xU(1)approx.S/sup 3/ x S/sup 1/ and the action of the conformal group upon it is identified with that of SU(2,2) on SU(2)xU(1). The equations are simplified by using as Ansatze gauge and Dirac fields that are both invariant under the following (or combinations of the following) subactions of SU(2,2): (i) left SU(2)/sub L/ translations, (ii) right SU(2)/sub R/ translations, (iii) the left action of SU(2)/sub L/xSU(2)/sub R/, and (iv) U(1) translations. All (real and complex) SU(2)/sub L/xU(1)/sub R/xU(1)-invariant solutions are obtained. The pullback of these solutions to Minkowski space leads to regular configurations with finite energy.

  2. On the instability of the n = 1 Einstein-Yang-Mills black holes and mathematically related systems.

    NASA Astrophysics Data System (ADS)

    Wald, R. M.

    1992-01-01

    The usual approach to analyze the linear stability of a static solution of some system of equations consists of searching for linearized solutions which satisfy suitable boundary conditions spatially and which grow exponentially in time. In the case of the n = 1 Einstein-Yang-Mills (EYM) black hole, an interesting situation occurs. There exists a perturbation which grows exponentially in time-and spatially decreases to zero at the horizon-but nevertheless is physically singular on the horizon. Thus, this unstable mode is unacceptable as initial data, and the question arises as to whether the n = 1 EYM black hole is stable. The author analyzes this issue here in the more general case. He proves that there exists smooth initial data of compact support in M which give rise to a solution which grows unboundedly with time. This implies that the n = 1 EYM black hole and other mathematically similar systems are unstable despite the nonexistence of physically acceptable exponentially growing modes.

  3. Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.

    PubMed

    Andreev, Oleg

    2009-05-29

    We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.

  4. Two-Loop Gell-Mann Function for General Renormalizable N = 1 Supersymmetric Theory, Regularized by Higher Derivatives

    NASA Astrophysics Data System (ADS)

    Shevtsova, Ekaterina

    2011-10-01

    For the general renormalizable N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, a two-loop β-function is calculated. It is shown that all integrals, needed for its obtaining are integrals of total derivatives.

  5. Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

    SciTech Connect

    Piotrowski, Mauricio J.; Piquini, Paulo; Da Silva, Juarez L. F.

    2010-04-15

    The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M{sub 13}. First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first-principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M{sub 13} structures. Several new lower energy configurations were identified, e.g., Pd{sub 13}, W{sub 13}, Pt{sub 13}, etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au{sub 13}, we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence

  6. Theory of topological quantum phase transitions in 3D noncentrosymmetric systems.

    PubMed

    Yang, Bohm-Jung; Bahramy, Mohammad Saeed; Arita, Ryotaro; Isobe, Hiroki; Moon, Eun-Gook; Nagaosa, Naoto

    2013-02-22

    We construct a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing occurs along directions with high crystalline symmetry. At the quantum critical point, the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point. Because of the anisotropic dispersion at quantum critical point, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.

  7. Exploring the surface reactivity of 3d metal endofullerenes: a density-functional theory study.

    PubMed

    Estrada-Salas, Rubén E; Valladares, Ariel A

    2009-09-24

    Changes in the preferential sites of electrophilic, nucleophilic, and radical attacks on the pristine C60 surface with endohedral doping using 3d transition metal atoms were studied via two useful reactivity indices, namely the Fukui functions and the molecular electrostatic potential. Both of these were calculated at the density functional BPW91 level of theory with the DNP basis set. Our results clearly show changes in the preferential reactivity sites on the fullerene surface when it is doped with Mn, Fe, Co, or Ni atoms, whereas there are no significant changes in the preferential reactivity sites on the C60 surface upon endohedral doping with Cu and Zn atoms. Electron affinities (EA), ionization potentials (IP), and HOMO-LUMO gaps (Eg) were also calculated to complete the study of the endofullerene's surface reactivity. These findings provide insight into endofullerene functionalization, an important issue in their application.

  8. GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies.

    PubMed

    Boudard, Mélanie; Bernauer, Julie; Barth, Dominique; Cohen, Johanne; Denise, Alain

    2015-01-01

    Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.

  9. The space of vacua of 3d N=3 abelian theories

    NASA Astrophysics Data System (ADS)

    Assel, Benjamin

    2017-08-01

    We use brane techniques to study the space of vacua of abelian 3d N=3 gauge theories. The coordinates on these spaces are the vevs of chiral monopole and meson operators, which are realized in the type IIB brane configuration of the theory by adding semi-infinite (1 , k) strings or F1 strings. The study of various brane setups allows us to determine a basis of chiral operators and chiral ring relations relevant to each branch of vacua, leading to the algebraic description of these branches. The method is mostly graphical and does not require actual computations. We apply it and provide explicit results in various examples. For linear quivers we find that the space of vacua has in general a collection of Coulomb-like branches, a Higgs branch and mixed branches. For circular quivers we find an extra branch, the geometric branch, parametrized by monopoles with equal magnetic charges in all U(1) nodes and meson operators. We explain how to include FI and mass deformations. We also study N=3 theories realized with ( p, q) 5-branes.

  10. Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence

    NASA Astrophysics Data System (ADS)

    Lelli, Simone; Maggiore, Michele; Rissone, Anna

    2003-04-01

    It is known that YM 2 with gauge group SU( N) is equivalent to a string theory with coupling gs=1/ N, order by order in the 1/ N expansion. We show how this result can be obtained from the bosonization of the fermionic formulation of YM 2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM 2 partition function of order exp{- kA/( πα' gs)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead strictly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM 2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.

  11. Wilson loops in supersymmetric gauge theories

    NASA Astrophysics Data System (ADS)

    Pestun, Vasily

    This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.

  12. Wave fluctuations in the system with some Yang-Mills condensates

    SciTech Connect

    Prokhorov, G.; Pasechnik, R.; Vereshkov, G.

    2016-12-15

    Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.

  13. Ergodic theory and experimental visualization of chaos in 3D flows

    NASA Astrophysics Data System (ADS)

    Sotiropoulos, Fotis; Mezic, Igor

    2000-11-01

    In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.

  14. Systematics of one-loop Yang-Mills diagrams from bosonic string amplitudes

    NASA Astrophysics Data System (ADS)

    Frizzo, Alberto; Magnea, Lorenzo; Russo, Rodolfo

    2001-06-01

    We present a general algorithm to compute off-shell, one-loop multigluon Green functions using bosonic string amplitudes. We identify and parametrize the regions in the space of moduli of one-loop Riemann surfaces that contribute to the field theory limit of string amplitudes. Each of these regions can be precisely associated with a Feynman-like scalar graph with cubic and quartic vertices, whose lines represent the joint propagation of ghosts and gluons. We give a procedure to compute the contribution of each graph to a gluon Green function, for arbitrarily polarized off-shell gluons, reducible and irreducible diagrams, planar and non-planar topologies. Explicit examples are given for up to six gluons.

  15. Charged D3-D7 plasmas: novel solutions, extremality and stability issues

    NASA Astrophysics Data System (ADS)

    Bigazzi, Francesco; Cotrone, Aldo L.; Tarrío, Javier

    2013-07-01

    We study finite temperature Super Yang-Mills (and more general gauge theories realized on intersecting D3-D7 branes) in the presence of dynamical massless fundamental matter fields at finite baryon charge density. We construct the holographic dual charged black hole solutions at first order in the flavor backreaction but exact in the charge density. The thermodynamical properties of the dual gauge theories coincide with the ones found in the usual charged D7-probe limit and the system turns out to be thermodynamically stable. By analyzing the higher order correction in the flavor backreaction, we provide a novel argument for the un-reliability of the charged probe approximation (and the present solution) in the extremality limit, i.e. at zero temperature. We then consider scalar mesonic-like bound states, whose spectrum is dual to that of linearized fluctuations of D7-brane worldvolume fields around our gravity backgrounds. In particular we focus on a scalar field saturating the Breitenlohner-Freedman bound in the flavorless limit, and coupled to fields dual to irrelevant operators. By looking at quasinormal modes of this scalar, we find no signals of instabilities in the regime of validity of the solutions.

  16. Localization and Dualities in Three-dimensional Superconformal Field Theories

    NASA Astrophysics Data System (ADS)

    Willett, Brian

    In this thesis we apply the technique of localization to three-dimensional N = 2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g , the Lie algebra of the gauge group of the theory, of a certain product of 1-loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries. In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to M-theory on an asymptotically AdS4 x S7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two three-dimensional field theories, namely, 3D mirror symmetry, Aharony duality, and Giveon-Kutasov duality. Here the dualities are typically between the IR limits of two Yang-Mills theories, which are strongly coupled in three dimensions since Yang-Mills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general three-dimensional theories in the form of the F-theorem, a conjectured analogy to the a-theorem in four dimensions and c-theorem in two dimensions, which is closely related to the localization computation.

  17. 3D imaging from theory to practice: the Mona Lisa story

    NASA Astrophysics Data System (ADS)

    Blais, Francois; Cournoyer, Luc; Beraldin, J.-Angelo; Picard, Michel

    2008-08-01

    The warped poplar panel and the technique developed by Leonardo to paint the Mona Lisa present a unique research and engineering challenge for the design of a complete optical 3D imaging system. This paper discusses the solution developed to precisely measure in 3D the world's most famous painting despite its highly contrasted paint surface and reflective varnish. The discussion focuses on the opto-mechanical design and the complete portable 3D imaging system used for this unique occasion. The challenges associated with obtaining 3D color images at a resolution of 0.05 mm and a depth precision of 0.01 mm are illustrated by exploring the virtual 3D model of the Mona Lisa.

  18. A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

    NASA Technical Reports Server (NTRS)

    Yates, John E.

    1991-01-01

    A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

  19. Basic theory on surface measurement uncertainty of 3D imaging systems

    NASA Astrophysics Data System (ADS)

    Beraldin, J. Angelo

    2009-01-01

    Three-dimensional (3D) imaging systems are now widely available, but standards, best practices and comparative data have started to appear only in the last 10 years or so. The need for standards is mainly driven by users and product developers who are concerned with 1) the applicability of a given system to the task at hand (fit-for-purpose), 2) the ability to fairly compare across instruments, 3) instrument warranty issues, 4) costs savings through 3D imaging. The evaluation and characterization of 3D imaging sensors and algorithms require the definition of metric performance. The performance of a system is usually evaluated using quality parameters such as spatial resolution/uncertainty/accuracy and complexity. These are quality parameters that most people in the field can agree upon. The difficulty arises from defining a common terminology and procedures to quantitatively evaluate them though metrology and standards definitions. This paper reviews the basic principles of 3D imaging systems. Optical triangulation and time delay (timeof- flight) measurement systems were selected to explain the theoretical and experimental strands adopted in this paper. The intrinsic uncertainty of optical distance measurement techniques, the parameterization of a 3D surface and systematic errors are covered. Experimental results on a number of scanners (Surphaser®, HDS6000®, Callidus CPW 8000®, ShapeGrabber® 102) support the theoretical descriptions.

  20. 3D kinematics using dual quaternions: theory and applications in neuroscience

    PubMed Central

    Leclercq, Guillaume; Lefèvre, Philippe; Blohm, Gunnar

    2013-01-01

    In behavioral neuroscience, many experiments are developed in 1 or 2 spatial dimensions, but when scientists tackle problems in 3-dimensions (3D), they often face problems or new challenges. Results obtained for lower dimensions are not always extendable in 3D. In motor planning of eye, gaze or arm movements, or sensorimotor transformation problems, the 3D kinematics of external (stimuli) or internal (body parts) must often be considered: how to describe the 3D position and orientation of these objects and link them together? We describe how dual quaternions provide a convenient way to describe the 3D kinematics for position only (point transformation) or for combined position and orientation (through line transformation), easily modeling rotations, translations or screw motions or combinations of these. We also derive expressions for the velocities of points and lines as well as the transformation velocities. Then, we apply these tools to a motor planning task for manual tracking and to the modeling of forward and inverse kinematics of a seven-dof three-link arm to show the interest of dual quaternions as a tool to build models for these kinds of applications. PMID:23443667

  1. Finite Element Methods and Multiphase Continuum Theory for Modeling 3D Air-Water-Sediment Interactions

    NASA Astrophysics Data System (ADS)

    Kees, C. E.; Miller, C. T.; Dimakopoulos, A.; Farthing, M.

    2016-12-01

    The last decade has seen an expansion in the development and application of 3D free surface flow models in the context of environmental simulation. These models are based primarily on the combination of effective algorithms, namely level set and volume-of-fluid methods, with high-performance, parallel computing. These models are still computationally expensive and suitable primarily when high-fidelity modeling near structures is required. While most research on algorithms and implementations has been conducted in the context of finite volume methods, recent work has extended a class of level set schemes to finite element methods on unstructured methods. This work considers models of three-phase flow in domains containing air, water, and granular phases. These multi-phase continuum mechanical formulations show great promise for applications such as analysis of coastal and riverine structures. This work will consider formulations proposed in the literature over the last decade as well as new formulations derived using the thermodynamically constrained averaging theory, an approach to deriving and closing macroscale continuum models for multi-phase and multi-component processes. The target applications require the ability to simulate wave breaking and structure over-topping, particularly fully three-dimensional, non-hydrostatic flows that drive these phenomena. A conservative level set scheme suitable for higher-order finite element methods is used to describe the air/water phase interaction. The interaction of these air/water flows with granular materials, such as sand and rubble, must also be modeled. The range of granular media dynamics targeted including flow and wave transmision through the solid media as well as erosion and deposition of granular media and moving bed dynamics. For the granular phase we consider volume- and time-averaged continuum mechanical formulations that are discretized with the finite element method and coupled to the underlying air

  2. Correlation of 3D volumetric positioning errors and temperature distributions: theory and measurement

    NASA Astrophysics Data System (ADS)

    Svoboda, O.; Bach, P.; Yang, J.; Wang, C.

    2006-11-01

    In a real machine shop environment and under various spindle loads, the machine thermal expansion may cause large 3D volumetric positioning errors. With an intelligent controller, it is possible to compensate these errors provide that the relations between the 3D volumetric positioning errors and the temperature distribution were measured. A laser vector measurement technique developed by Optodyne was used for a quick measurement of 3D volumetric positioning errors of a CNC machining center under various spindle loads, machine movement and ambient conditions. Correlation calculations were used to determine the key temperatures and the various positioning errors. Preliminary results showed that large machine temperature changes caused somewhat small straightness error changes but large squareness error changes. Using the measured position errors, several error maps could be generated. Compensation tables at an actual thermal state can be interpolated to achieve higher accuracy at various thermal loadings.

  3. Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

    NASA Astrophysics Data System (ADS)

    Guimaraes, M. S.; Mintz, B. W.; Sorella, S. P.

    2015-06-01

    We investigate the dimension two condensate ⟨ϕ¯ia bϕia b-ω¯ia bωia b⟩ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate ⟨ϕ¯i a bϕia b-ω¯i a bωia b⟩ is plagued by a nonintegrable IR divergence in 3 D , while in 4 D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter γ2. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.

  4. Assessing the performance of density functional theory for the electronic structure of metal-salens: the 3d(0)-metals.

    PubMed

    Sears, John S; Sherrill, C David

    2008-04-17

    A series of metal-salen complexes of the 3d(0) metals Sc(III), Ti(IV), V(V), Cr(VI), and Mn(VII) have been explored using high-level electronic structure methods including coupled-cluster theory with singles, doubles, and perturbative triples as well as complete active-space third-order perturbation theory. The performance of three common density functional theory approaches has been assessed for both the geometries and the relative energies of the low-lying electronic states. The nondynamical correlation effects are demonstrated to be extremely large in all of the systems examined. Although density functional theory provides reasonable results for some of the systems, the overall agreement is quite poor. This said, the density functional theory approaches are shown to outperform the single-reference perturbation theory and coupled-cluster theory approaches for cases of strong nondynamical correlation.

  5. Perturbative gauge theory at null infinity

    NASA Astrophysics Data System (ADS)

    Adamo, Tim; Casali, Eduardo

    2015-06-01

    We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.

  6. 4d/3d reduction of s-confining theories: the role of the "exotic" D instantons

    NASA Astrophysics Data System (ADS)

    Amariti, Antonio

    2016-02-01

    The reduction of 4d Seiberg duality to 3d by compactification on a circle is possible if finite size effects are considered. These effects boil down to the contribution of KK monopole operators acting as instantons in 3d, and they are crucial to preserve the 4d duality in 3d. This mechanism has been reproduced in string theory by T-duality on the type IIA brane setup. In some cases the 4d dual "magnetic" theories are IR confined descriptions of the UV gauge theories. In these cases the monopoles are absent in the IR dynamics and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also from the "exotic" contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we provide the interpretation of the mechanism in terms of localization.

  7. Transfer of Learning between 2D and 3D Sources during Infancy: Informing Theory and Practice

    ERIC Educational Resources Information Center

    Barr, Rachel

    2010-01-01

    The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a two-dimensional (2D) representation and a three-dimensional (3D) object. Understanding the conditions under which young children might accomplish this…

  8. The Cognitive Apprenticeship Theory for the Teaching of Mathematics in an Online 3D Virtual Environment

    ERIC Educational Resources Information Center

    Bouta, Hara; Paraskeva, Fotini

    2013-01-01

    Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective.…

  9. Transfer of Learning between 2D and 3D Sources during Infancy: Informing Theory and Practice

    ERIC Educational Resources Information Center

    Barr, Rachel

    2010-01-01

    The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a two-dimensional (2D) representation and a three-dimensional (3D) object. Understanding the conditions under which young children might accomplish this…

  10. The Cognitive Apprenticeship Theory for the Teaching of Mathematics in an Online 3D Virtual Environment

    ERIC Educational Resources Information Center

    Bouta, Hara; Paraskeva, Fotini

    2013-01-01

    Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective.…

  11. Confinement and lattice gauge theory

    SciTech Connect

    Creutz, M

    1980-06-01

    The motivation for formulating gauge theories on a lattice to study non-perturbative phenomena is reviewed, and recent progress supporting the compatibility of asymptotic freedom and quark confinement in the standard SU(3) Yang-Mills theory of the strong interaction is discussed.

  12. Octanol-Water Partition Coefficient from 3D-RISM-KH Molecular Theory of Solvation with Partial Molar Volume Correction.

    PubMed

    Huang, WenJuan; Blinov, Nikolay; Kovalenko, Andriy

    2015-04-30

    The octanol-water partition coefficient is an important physical-chemical characteristic widely used to describe hydrophobic/hydrophilic properties of chemical compounds. The partition coefficient is related to the transfer free energy of a compound from water to octanol. Here, we introduce a new protocol for prediction of the partition coefficient based on the statistical-mechanical, 3D-RISM-KH molecular theory of solvation. It was shown recently that with the compound-solvent correlation functions obtained from the 3D-RISM-KH molecular theory of solvation, the free energy functional supplemented with the correction linearly related to the partial molar volume obtained from the Kirkwood-Buff/3D-RISM theory, also called the "universal correction" (UC), provides accurate prediction of the hydration free energy of small compounds, compared to explicit solvent molecular dynamics [ Palmer , D. S. ; J. Phys.: Condens. Matter 2010 , 22 , 492101 ]. Here we report that with the UC reparametrized accordingly this theory also provides an excellent agreement with the experimental data for the solvation free energy in nonpolar solvent (1-octanol) and so accurately predicts the octanol-water partition coefficient. The performance of the Kovalenko-Hirata (KH) and Gaussian fluctuation (GF) functionals of the solvation free energy, with and without UC, is tested on a large library of small compounds with diverse functional groups. The best agreement with the experimental data for octanol-water partition coefficients is obtained with the KH-UC solvation free energy functional.

  13. Ligand mapping on protein surfaces by the 3D-RISM theory: toward computational fragment-based drug design.

    PubMed

    Imai, Takashi; Oda, Koji; Kovalenko, Andriy; Hirata, Fumio; Kidera, Akinori

    2009-09-02

    In line with the recent development of fragment-based drug design, a new computational method for mapping of small ligand molecules on protein surfaces is proposed. The method uses three-dimensional (3D) spatial distribution functions of the atomic sites of the ligand calculated using the molecular theory of solvation, known as the 3D reference interaction site model (3D-RISM) theory, to identify the most probable binding modes of ligand molecules. The 3D-RISM-based method is applied to the binding of several small organic molecules to thermolysin, in order to show its efficiency and accuracy in detecting binding sites. The results demonstrate that our method can reproduce the major binding modes found by X-ray crystallographic studies with sufficient precision. Moreover, the method can successfully identify some binding modes associated with a known inhibitor, which could not be detected by X-ray analysis. The dependence of ligand-binding modes on the ligand concentration, which essentially cannot be treated with other existing computational methods, is also investigated. The results indicate that some binding modes are readily affected by the ligand concentration, whereas others are not significantly altered. In the former case, it is the subtle balance in the binding affinity between the ligand and water that determines the dominant ligand-binding mode.

  14. Wave optics theory and 3-D deconvolution for the light field microscope.

    PubMed

    Broxton, Michael; Grosenick, Logan; Yang, Samuel; Cohen, Noy; Andalman, Aaron; Deisseroth, Karl; Levoy, Marc

    2013-10-21

    Light field microscopy is a new technique for high-speed volumetric imaging of weakly scattering or fluorescent specimens. It employs an array of microlenses to trade off spatial resolution against angular resolution, thereby allowing a 4-D light field to be captured using a single photographic exposure without the need for scanning. The recorded light field can then be used to computationally reconstruct a full volume. In this paper, we present an optical model for light field microscopy based on wave optics, instead of previously reported ray optics models. We also present a 3-D deconvolution method for light field microscopy that is able to reconstruct volumes at higher spatial resolution, and with better optical sectioning, than previously reported. To accomplish this, we take advantage of the dense spatio-angular sampling provided by a microlens array at axial positions away from the native object plane. This dense sampling permits us to decode aliasing present in the light field to reconstruct high-frequency information. We formulate our method as an inverse problem for reconstructing the 3-D volume, which we solve using a GPU-accelerated iterative algorithm. Theoretical limits on the depth-dependent lateral resolution of the reconstructed volumes are derived. We show that these limits are in good agreement with experimental results on a standard USAF 1951 resolution target. Finally, we present 3-D reconstructions of pollen grains that demonstrate the improvements in fidelity made possible by our method.

  15. Wave optics theory and 3-D deconvolution for the light field microscope

    PubMed Central

    Broxton, Michael; Grosenick, Logan; Yang, Samuel; Cohen, Noy; Andalman, Aaron; Deisseroth, Karl; Levoy, Marc

    2013-01-01

    Light field microscopy is a new technique for high-speed volumetric imaging of weakly scattering or fluorescent specimens. It employs an array of microlenses to trade off spatial resolution against angular resolution, thereby allowing a 4-D light field to be captured using a single photographic exposure without the need for scanning. The recorded light field can then be used to computationally reconstruct a full volume. In this paper, we present an optical model for light field microscopy based on wave optics, instead of previously reported ray optics models. We also present a 3-D deconvolution method for light field microscopy that is able to reconstruct volumes at higher spatial resolution, and with better optical sectioning, than previously reported. To accomplish this, we take advantage of the dense spatio-angular sampling provided by a microlens array at axial positions away from the native object plane. This dense sampling permits us to decode aliasing present in the light field to reconstruct high-frequency information. We formulate our method as an inverse problem for reconstructing the 3-D volume, which we solve using a GPU-accelerated iterative algorithm. Theoretical limits on the depth-dependent lateral resolution of the reconstructed volumes are derived. We show that these limits are in good agreement with experimental results on a standard USAF 1951 resolution target. Finally, we present 3-D reconstructions of pollen grains that demonstrate the improvements in fidelity made possible by our method. PMID:24150383

  16. A 3d-3d appetizer

    NASA Astrophysics Data System (ADS)

    Pei, Du; Ye, Ke

    2016-11-01

    We test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d N=2 "Lens space theory" T [ L( p, 1)] and the partition function of complex Chern-Simons theory on L( p, 1). In particular, for p = 1, we show how the familiar S 3 partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[ L( p, 1)] becomes a constant independent of p. In addition, we study T[ L( p, 1)] on the squashed three-sphere S b 3 . This enables us to see clearly, at the level of partition function, to what extent G ℂ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.

  17. A new algorithm for determining 3D biplane imaging geometry: theory and implementation

    NASA Astrophysics Data System (ADS)

    Singh, Vikas; Xu, Jinhui; Hoffmann, Kenneth R.; Xu, Guang; Chen, Zhenming; Gopal, Anant

    2005-04-01

    Biplane imaging is a primary method for visual and quantitative assessment of the vasculature. A key problem called Imaging Geometry Determination problem (IGD for short) in this method is to determine the rotation-matrix R and the translation-vector t which relate the two coordinate systems. In this paper, we propose a new approach, called IG-Sieving, to calculate R and t using corresponding points in the two images. Our technique first generates an initial estimate of R and t from the gantry angles of the imaging system, and then optimizes them by solving an optimal-cell-search problem in a 6-D parametric space (three variables defining R plus the three variables of t). To efficiently find the optimal imaging geometry (IG) in 6-D, our approach divides the high dimensional search domain into a set of lower-dimensional regions, thereby reducing the optimal-cell-search problem to a set of optimization problems in 3D sub-spaces. For each such sub-space, our approach first applies efficient computational geometry techniques to identify "possibly-feasible"" IG"s, and then uses a criterion we call fall-in-number to sieve out good IGs. We show that in a bounded number of optimization steps, a (possibly infinite) set of near-optimal IGs can be determined. Simulation results indicate that our method can reconstruct 3D points with average 3D center-of-mass errors of about 0.8cm for input image-data errors as high as 0.1cm. More importantly, our algorithm provides a novel insight into the geometric structure of the solution-space, which could be exploited to significantly improve the accuracy of other biplane algorithms.

  18. Quantum tunneling of spin-1 particles from a 5D Einstein-Yang-Mills-Gauss-Bonnet black hole beyond semiclassical approximation

    NASA Astrophysics Data System (ADS)

    Jusufi, K.

    2016-12-01

    In the present paper we study the Hawking radiation as a quantum tunneling effect of spin-1 particles from a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (5D EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results in a set of five differential equations, and reproduces, in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the entropy of the EYMGB black hole and show that the quantum corrected specific heat indicates the possible existence of a remnant.

  19. Holographic Screening Length on Parallel Motion of Quark-Antiquark Pair in Four Dimensional Strongly Coupled = 4 super-Yang-Mills plasma

    NASA Astrophysics Data System (ADS)

    Nata Atmaja, Ardian

    2014-10-01

    We study the screening length of a quark-antiquark pair moving in a strongly coupled hot plasma of = 4 super-Yang-Mills using AdS/CFT correspondence where the background metric is five dimensional AdS black hole. We take the string solution as such the separation length L of quark-antiquark pair is parallel to the string velocity v. The screening length and the bound energy are computed numerically using Mathematica. We find that the plots are bounded from below by some functions that are related to the momentum flow of the drag force configuration Pc. We compare the result by computing the screening length in the quark-antiquark reference frame by boosting the AdS black hole.

  20. From 3D topological quantum field theories to 4D models with defects

    NASA Astrophysics Data System (ADS)

    Delcamp, Clement; Dittrich, Bianca

    2017-06-01

    (2 + 1) dimensional topological quantum field theories (TQFTs) with defect excitations are by now quite well understood, while many questions are still open for (3 + 1) dimensional TQFTs. Here we propose a strategy to lift states and operators of a (2 + 1) dimensional TQFT to states and operators of a (3 + 1) dimensional theory with defects. The main technical tool is Heegaard splittings, which allow us to encode the topology of a three-dimensional manifold with line defects into a two-dimensional Heegaard surface. We apply this idea to the example of BF theory which describes locally flat connections. This shows in particular how the curvature excitation generating surface operators of the (3 + 1) dimensional theory can be obtained from closed ribbon operators of the (2 + 1) dimensional BF theory. We hope that this technique allows the construction and study of more general models based on unitary fusion categories.

  1. 3d N = 1 Chern-Simons-matter theory and localization

    NASA Astrophysics Data System (ADS)

    Tsimpis, Dimitrios; Zhu, Yaodong

    2016-10-01

    We consider the most general, classically-conformal, three-dimensional N = 1 Chern-Simons-matter theory with global symmetry Sp (2) and gauge group U (N) × U (N). We show that the Lagrangian in the on-shell formulation of the theory admits one more free parameter as compared to the theory formulated in off-shell N = 1 superspace. The theory on T3 can be formally localized. We partially carry out the localization procedure for the theory on T3 with periodic boundary conditions. In particular we show that restricting to the saddle points with vanishing gauge connection gives a trivial contribution to the partition function, i.e. the bosonic and fermionic contributions exactly cancel each other.

  2. 3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

    NASA Astrophysics Data System (ADS)

    McLaughlin, J. A.; Ferguson, J. S. L.; Hood, A. W.

    2008-09-01

    This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[ x, ɛ y,-( ɛ+1) z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ɛ. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ɛ determines where the wave accumulation will occur: fan plane ( ɛ=1), along the x-axis (0< ɛ<1) or along the y-axis ( ɛ>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.

  3. Localization and visualization of excess chemical potential in statistical mechanical integral equation theory 3D-HNC-RISM.

    PubMed

    Du, Qi-Shi; Liu, Peng-Jun; Huang, Ri-Bo

    2008-02-01

    In this study the excess chemical potential of the integral equation theory, 3D-RISM-HNC [Q. Du, Q. Wei, J. Phys. Chem. B 107 (2003) 13463-13470], is visualized in three-dimensional form and localized at interaction sites of solute molecule. Taking the advantage of reference interaction site model (RISM), the calculation equations of chemical excess potential are reformulized according to the solute interaction sites s in molecular space. Consequently the solvation free energy is localized at every interaction site of solute molecule. For visualization of the 3D-RISM-HNC calculation results, the excess chemical potentials are described using radial and three-dimensional diagrams. It is found that the radial diagrams of the excess chemical potentials are more sensitive to the bridge functions than the radial diagrams of solvent site density distributions. The diagrams of average excess chemical potential provide useful information of solute-solvent electrostatic and van der Waals interactions. The local description of solvation free energy at active sites of solute in 3D-RISM-HNC may broaden the application scope of statistical mechanical integral equation theory in solution chemistry and life science.

  4. Local mode theory for C3v molecules: CH3D, CHD3, SiH3D, and SiHD3

    NASA Astrophysics Data System (ADS)

    Halonen, L.; Child, M. S.

    1983-11-01

    A three parameter potential model for the stretching vibrations of AH3D and AHD3 species (A=C or Si) is shown to give good agreement with experimental data thereby justifying predictions for the term values of unobserved levels. The structures of the overtone manifolds for different molecules are rationalized by means of an AH3 local mode to normal mode correlation diagram.

  5. Flat holography: aspects of the dual field theory

    NASA Astrophysics Data System (ADS)

    Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya

    2016-12-01

    Assuming the existence of a field theory in D dimensions dual to ( D + 1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D = 4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

  6. Operator counting and eigenvalue distributions for 3D supersymmetric gauge theories

    NASA Astrophysics Data System (ADS)

    Gulotta, Daniel R.; Herzog, Christopher P.; Pufu, Silviu S.

    2011-11-01

    We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with mathcal{N} = {2} instead of mathcal{N} = {3} supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.

  7. 3d-3d correspondence revisited

    DOE PAGES

    Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; ...

    2016-04-21

    In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

  8. 3d-3d correspondence revisited

    SciTech Connect

    Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr

    2016-04-21

    In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

  9. Induced Polarization with Electromagnetic Coupling: 3D Spectral Imaging Theory, EMSP Project No. 73836

    SciTech Connect

    Morgan, F. Dale; Sogade, John

    2004-12-14

    This project was designed as a broad foundational study of spectral induced polarization (SIP) for characterization of contaminated sites. It encompassed laboratory studies of the effects of chemistry on induced polarization, development of 3D forward modeling and inversion codes, and investigations of inductive and capacitive coupling problems. In the laboratory part of the project a physico-chemical model developed in this project was used to invert laboratory IP spectra for the grain size and the effective grain size distribution of the sedimentary rocks as well as the formation factor, porosity, specific surface area, and the apparent fractal dimension. Furthermore, it was established that the IP response changed with the solution chemistry, the concentration of a given solution chemistry, valence of the constituent ions, and ionic radius. In the field part of the project, a 3D complex forward and inverse model was developed. It was used to process data acquired at two frequencies (1/16 Hz and 1/ 4Hz) in a cross-borehole configuration at the A-14 outfall area of the Savannah River Site (SRS) during March 2003 and June 2004. The chosen SRS site was contaminated with Tetrachloroethylene (TCE) and Trichloroethylene (PCE) that were disposed in this area for several decades till the 1980s. The imaginary conductivity produced from the inverted 2003 data correlated very well with the log10 (PCE) concentration derived from point sampling at 1 ft spacing in five ground-truth boreholes drilled after the data acquisition. The equivalent result for the 2004 data revealed that there were significant contaminant movements during the period March 2003 and June 2004, probably related to ground-truth activities and nearby remediation activities. Therefore SIP was successfully used to develop conceptual models of volume distributions of PCE/TCE contamination. In addition, the project developed non-polarizing electrodes that can be deployed in boreholes for years. A total of 28

  10. Exact results for vortex loop operators in 3d supersymmetric theories

    NASA Astrophysics Data System (ADS)

    Drukker, Nadav; Okuda, Takuya; Passerini, Filippo

    2014-07-01

    Three dimensional field theories admit disorder line operators, dubbed vortex loop operators. They are defined by the path integral in the presence of prescribed singularities along the defect line. We study half-BPS vortex loop operators for = 2 supersymmetric theories on 3, its deformation and 1 × 2. We construct BPS vortex loops defined by the path integral with a fixed gauge or flavor holonomy for infinitesimal curves linking the loop. It is also possible to include a singular profile for matter fields. For vortex loops defined by holonomy, we perform supersymmetric localization by calculating the fluctuation modes, or alternatively by applying the index theory for transversally elliptic operators. We clarify how the latter method works in situations without fixed points of relevant isometries. Abelian mirror symmetry transforms Wilson and vortex loops in a specific way. In particular an ordinary Wilson loop transforms into a vortex loop for a flavor symmetry. Our localization results confirm the predictions of abelian mirror symmetry.

  11. Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory

    NASA Astrophysics Data System (ADS)

    Ebrahimi, Farzad; Barati, Mohammad Reza

    2016-09-01

    This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori-Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton's principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.

  12. 3D SIMULATIONS OF REALISTIC POWER HALOS IN MAGNETOHYDROSTATIC SUNSPOT ATMOSPHERES: LINKING THEORY AND OBSERVATION

    SciTech Connect

    Rijs, Carlos; Przybylski, Damien; Moradi, Hamed; Cally, Paul S.; Shelyag, Sergiy; Rajaguru, S. P.

    2016-01-20

    The well-observed acoustic halo is an enhancement in time-averaged Doppler velocity and intensity power with respect to quiet-Sun values that is prominent for the weak and highly inclined field around the penumbra of sunspots and active regions. We perform 3D linear wave modeling with realistic distributed acoustic sources in a magnetohydrostatic sunspot atmosphere and compare the resultant simulation enhancements with multiheight SDO observations of the phenomenon. We find that simulated halos are in good qualitative agreement with observations. We also provide further proof that the underlying process responsible for the halo is the refraction and return of fast magnetic waves that have undergone mode conversion at the critical a = c atmospheric layer. In addition, we also find strong evidence that fast Alfvén mode conversion plays a significant role in the structure of the halo, taking energy away from photospheric and chromospheric heights in the form of field-aligned Alfvén waves. This conversion process may explain the observed “dual-ring” halo structure at higher (>8 mHz) frequencies.

  13. A Quasi-3-D Theory for Impedance Eduction in Uniform Grazing Flow

    NASA Technical Reports Server (NTRS)

    Watson, W. R.; Jones, M. G.; Parrott, T. L.

    2005-01-01

    A 2-D impedance eduction methodology is extended to quasi-3-D sound fields in uniform or shearing mean flow. We introduce a nonlocal, nonreflecting boundary condition to terminate the duct and then educe the impedance by minimizing an objective function. The introduction of a parallel, sparse, equation solver significantly reduces the wall clock time for educing the impedance when compared to that of the sequential band solver used in the 2-D methodology. The accuracy, efficiency, and robustness of the methodology is demonstrated using two examples. In the first example, we show that the method reproduces the known impedance of a ceramic tubular test liner. In the second example, we illustrate that the approach educes the impedance of a four-segment liner where the first, second, and fourth segments consist of a perforated face sheet bonded to honeycomb, and the third segment is a cut from the ceramic tubular test liner. The ability of the method to educe the impedances of multisegmented liners has the potential to significantly reduce the amount of time and cost required to determine the impedance of several uniform liners by allowing them to be placed in series in the test section and to educe the impedance of each segment using a single numerical experiment. Finally, we probe the objective function in great detail and show that it contains a single minimum. Thus, our objective function is ideal for use with local, inexpensive, gradient-based optimizers.

  14. Comparison of 3D Classical Trajectory and Transition-State Theory Reaction Cross Sections

    DOE R&D Accomplishments Database

    Koeppl, G. W.; Karplus, Martin

    1970-10-01

    Although there is excellent agreement for a system such as H+H{sub 2} --> H{sub 2}+H, in which both the potential and the particle masses are symmetric, significant deviations occur for more asymmetric reactions. A detailed analysis show that the calculated differences are from the violation of two assumptions of transition-state theory.

  15. Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

    SciTech Connect

    Vescovi, D.; Berzi, D.; Richard, P.

    2014-05-15

    We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

  16. Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes

    SciTech Connect

    Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H.; Roiban, R.

    2012-02-15

    We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.

  17. Coulomb branches for rank 2 gauge groups in 3 d N=4 gauge theories

    NASA Astrophysics Data System (ADS)

    Hanany, Amihay; Sperling, Marcus

    2016-08-01

    The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.

  18. Refined 3d-3d correspondence

    NASA Astrophysics Data System (ADS)

    Alday, Luis F.; Genolini, Pietro Benetti; Bullimore, Mathew; van Loon, Mark

    2017-04-01

    We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N = 2 theories constructed from boundary conditions and interfaces in a 4d N = 2∗ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2∗ theory. In the presence of a mass parameter cfor the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.

  19. Induced Polarization with Electromagnetic Coupling: 3D Spectral Imaging Theory EMSP Project No. 73836

    SciTech Connect

    Morgan, F. Dale

    2003-06-01

    considered invertible by our existing 2D/3D complex resistivity codes. The results of this exercise were inconclusive because the ground-truthing phase of the operation failed to detect ny concentration of NAPL above a requisite threshold of 40-50{micro}g/g. It is our understanding that this threshold level is based upon analytic chemical partition analysis, which is dependent upon the physicochemical properties of the soil, its pore-fluid, and organic constituents [Cohen and Mercer, 1993], and thus represents a necessary and sufficient condition to confirm the presence of NAPL. Therefore, since the round-truthing phase never found PCE concentrations in excess of {approx}3mg/g, there is no irrefutable evidence of NAPL; hence, the objective of the FY01 exercise could not be completed. Nonetheless, ERL's conversion results agree well with the ground truth considering the sparseness of the CRS boreholes, low concentrations of ''PCE'' (< 3{micro}g/g), and despite poor electrodes. Note that the displacement of the enter of the SIP phase anomaly from that of the ground truth data might be due to inaccuracies in the SIP conversion (which we are still working on improving) or sampling depth errors during the ground-truthing phase which could cumulatively amount to a meter or more. (3) As a continuation of the FY01 efforts, another et of surface and borehole SIP measurements were planned at another SRS site during FY02, which unlike he FY01 site,had been verified to have substantial DNAPL presence by SRS engineers. The plan to use phoenix Geophysics SIP equipment could not materialize because Phoenix discontinued its SIP line and planned to introduce a new line in the Spring/Summer of 2003, which will be too late for us. So our planned second fieldwork of FY02 defaults again to Zonge Engineering and Research Organization equipment. (4) developments on the modeling and inversion of the new complex resistivity code, that will incorporate conductive coupling, stalled to give way to the

  20. Gauge theories in anti-selfdual variables

    NASA Astrophysics Data System (ADS)

    Bochicchio, Marco; Pilloni, Alessandro

    2013-09-01

    Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure Yang-Mills from its original definition in = 1 supersymmetric Yang-Mills. We study here the perturbative one-particle irreducible effective action in the anti-selfdual variables of any gauge theory, in particular pure Yang-Mills, QCD and = 1 supersymmetric Yang-Mills. We prove that the one-loop one-particle irreducible effective action of a gauge theory mapped to the anti-selfdual variables in any gauge is identical to the one of the original theory. This is due to the conspiracy between the Jacobian of the change to the anti-selfdual variables and an extra functional determinant that arises from the non-linearity of the coupling of the anti-selfdual curvature to an external source in the Legendre transform that defines the one-particle irreducible effective action. Hence we establish the one-loop perturbative equivalence of the mapped and original theories on the basis of the identity of the one-loop one-particle irreducible effective actions. Besides, we argue that the identity of the perturbative one-particle irreducible effective actions extends order by order in perturbation theory.