Surface-invariants in 2D classical Yang-Mills theory
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.
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.
Gauged supersymmetries in Yang-Mills theory
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.
Gravitino interactions from Yang-Mills theory
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.
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.
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.
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.
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.
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.
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.
Path integral regularization of pure Yang-Mills theory
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.
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.
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.
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.
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.
Hamiltonian flow in Coulomb gauge Yang-Mills theory
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.
Deconfinement in Yang-Mills Theory through Toroidal Compactification
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.
Infrared propagators of Yang-Mills theory from perturbation theory
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.
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.
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.
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...
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.
Transport coefficients in Yang-Mills theory and QCD.
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.
MONOPOLES AND DYONS IN THE PURE EINSTEIN YANG MILLS THEORY
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.
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.
Width of the confining string in Yang-Mills theory.
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.
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.
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.
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.
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.
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.
Is the ground state of Yang-Mills theory Coulombic?
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.
Instanton Effective Action in Deformed Super Yang-Mills Theories
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.
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.
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.
Infrared singularities in Landau gauge Yang-Mills theory
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.
Composite strings in (2+1)-dimensional anisotropic weakly coupled Yang-Mills theory
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.
Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory
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.
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.
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.
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.
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.
Renormalizability of Yang-Mills theory with Lorentz violation and gluon mass generation
NASA Astrophysics Data System (ADS)
Santos, T. R. S.; Sobreiro, R. F.
2015-01-01
We show that pure Yang-Mills theories with Lorentz violation are renormalizable to all orders in perturbation theory. To do this, we employ the algebraic renormalization technique. Specifically, we control the breaking terms with a suitable set of external sources, which eventually attain certain physical values. The Abelian case is also analyzed as a starting point. The main result is that the renormalizability of the usual Maxwell and Yang-Mills sectors are both left unchanged. Furthermore, in contrast to Lorentz-violating QED, the C P T -odd violation sector of Yang-Mills theories renormalizes independently. Moreover, the method induces mass terms for the gauge field in a natural way, while the photon remains massless (at least in the sense of a Proca-like term). The entire analysis is carried out in the Landau gauge.
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.
Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
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.
Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge--Revisited
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.
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
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.
Center-stabilized Yang-Mills Theory:Confinement and Large N Volume Independence
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.
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.
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.
Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory at Strong Coupling
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.
Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge
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.
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.
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.
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.
Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
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.
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.
Quantum Metamorphosis of a Conformal Transformation in D3-Brane Yang-Mills Theory
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}
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.
Four-loop dressing phase of N=4 super-Yang-Mills theory
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)
Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.
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.
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.
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.
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.
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.
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.
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.
Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.
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.
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.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
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.
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.
Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory
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.
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.
Z{sub 2} monopoles in SU(n) Yang-Mills-Higgs theories
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.}
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
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.
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.
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
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.
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.
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.
Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space
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.
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.
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.
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.
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.
Massless and massive three-dimensional super Yang-Mills theory and mini-twistor string theory
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.
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.
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.
`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.
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.
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 .
Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory
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.
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.
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.
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.
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.
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.
= 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.
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.
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
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.
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.
Integration of Kaluza-Klein modes in Yang-Mills theories
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.
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.
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.
Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory
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.
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
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.
Duality-symmetric supersymmetric Yang-Mills theory in three dimensions
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.
Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship
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.
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.
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.
Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD
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.
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.
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.
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
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.
Towards the large N limit of pure Nu = 1 super Yang-Mills theory.
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.
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.
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.
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.
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.
Lo, C.Y.
1981-01-15
In this paper, we study the apparent discrepancy between Feynman diagrams and the eikonal formulas, and the apparent paradox between the eikonal formulas and the s-u crossing symmetry. We analyze the generalized leading-term approximation (GLA), which generates the terms of the eikonal formulas from Feynman diagrams. This analysis is done through using the techniques of decomposing diagrammatically the isospin factors (or group-theoretical weights in general) of Feynman diagrams. As a result, we modify the GLA into a generalized complex leading-term approximation. We calculate, with this new formalism, the high-energy limit (s..-->..infinity with t fixed) of the vector-meson--vector-meson elastic amplitude of a Yang-Mills theory with SU(2) symmetry through tenth perturbative order. With this new method, we resolve the apparent discrepancy and paradox mentioned above. This method is generalizable to other non-Abelian gauge theories.
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.
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.
Lattice study of two-dimensional N=(2,2) super Yang-Mills theory at large N
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.
Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Conformal kernel for the next-to-leading-order BFKL equation in N=4 super Yang-Mills theory
Balitsky, Ian; Chirilli, Giovanni A.
2009-02-01
Using the requirement of Moebius invariance of N=4 super Yang-Mills amplitudes in the Regge limit, we restore the explicit form of the conformal next-to-leading-order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel out of the eigenvalues known from the forward next-to-leading-order BFKL result.
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.
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
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.
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.
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.
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 .
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.
The framed Standard Model (I) — A physics case for framing the Yang-Mills theory?
NASA Astrophysics Data System (ADS)
Chan, Hong-Mo; Tsou, Sheung Tsun
2015-10-01
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: the standard Higgs scalar as the framon in the electroweak sector; a global su˜(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: CKM mixing and neutrino oscillations, hierarchical masses for quarks and leptons, a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.
The Framed Standard Model (I) -- A Physics Case for Framing the Yang-Mills Theory?
NASA Astrophysics Data System (ADS)
Chan, Hong-Mo; Tsou, Sheung Tsun
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global widetilde{su}(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarchical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
YANG-MILLS FIELDS AND THE LATTICE.
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.
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.
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.
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.
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.
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.
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.
Non-Abelian strings in supersymmetric Yang-Mills
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.
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.
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.
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.
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.
Exotic polarizations of D2 branes and oblique vacua of (2+1)-dimensional super Yang-Mills theory
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.
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
No-go for partially massless spin-2 Yang-Mills
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.
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.
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.
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.
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.
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.
Fate of Yang-Mills black hole in early Universe
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.
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.
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.
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.
Understanding the Yang-Mills ground state: The origin of colour confinement
NASA Astrophysics Data System (ADS)
Preparata, Giuliano
1988-01-01
The essential magnetic instability of the perturbative ground state of a non-abelian Yang-Mills theory recently discovered, is shown to lead to a family of degenerate states, the Savvidy states, where the Yang-Mills fields undergo an infinite (when the ultraviolet cut-off Λ-->∞M) condensation process. These states build up the real Yang-Mills ground state, in which colour is confined and governed by the effective lagrangian of anisotropic chromodynamics (ACD), proposed by the present author a few years ago. This appears to solve the problem of confinement in QCD. On leave of absence from Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy.
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 ).
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.
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.
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.
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.
Classical Yang-Mills Mechanics: Instant vs. Light-cone Form
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.
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.
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.
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...
Lattice super-Yang-Mills using domain wall fermions in the chiral limit
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.
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.
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.
Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis
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.
String scattering in flat space and a scaling limit of Yang-Mills correlators
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.
NASA Astrophysics Data System (ADS)
Baulieu, Laurent
1996-02-01
We construct a framework which unifies in pairs the fields and anti-fields of the Batalin and Vilkovisky quantization method. We consider gauge theories of p-forms coupled to Yang-Mills fields. Our algorithm generates many topological models of the Chern-Simons type or of the Donaldson-Witten type. Some of these models can undergo a partial breaking of their topological symmetries. We investigate the properties of 2D gravity in the Batalin and Vilkovisky quantization scheme. We find a structure which satisfies the holomorphic factorization and also properties analogous to those existing in the topological theories of forms. New conformal fields are introduced with their invariant action.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Gravity and Yang-Mills amplitude relations
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Conformally flat Einstein-Yang-Mills-Higgs solutions with spherical symmetry
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.
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.
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.
On the ground state of Yang-Mills theory
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.
Ice limit of Coulomb gauge Yang-Mills theory
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.
F-theory and 2d (0, 2) theories
NASA Astrophysics Data System (ADS)
Schäfer-Nameki, Sakura; Weigand, Timo
2016-05-01
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N = (0 , 2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0 , 2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0 , 2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0 , 2) GLSM is realized via different T-branes or gluing data in F-theory.
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.
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 .
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.
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.
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.
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.
Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction
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.
- 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.
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.
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.
Yang-Mills instantons sitting on a Ricci-flat worldspace of double D4-branes
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.
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.
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).
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.
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).
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.
An instability of hyperbolic space under the Yang-Mills flow
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.
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
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.
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.
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
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.
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.
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
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.
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.
Some exact solutions of (2+1)-dimensional Yang-Mills equations with the Chern-Simons term
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.
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.
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.
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.
Anisotropic N=4 Super-Yang-Mills Plasma and Its Instabilities
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.
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.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Density functional theory for polymeric systems in 2D.
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-22
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.
On the spectrum of 2D conformal field theories
NASA Astrophysics Data System (ADS)
Gepner, Doron
Possible unitary statistical models and SU(2) current algebra theories are classified up to certain "levels" of the Virasoro and Kac-Moody algebras. A connection that is found between the Virasoro and SU(2) Kac-Moody characters is used to generate unitary statistical models from the SU(2) theories. Using the "fusion rules" of the operator product algebra of these theories, we are able to check the consistency of the solutions, and to write down their operator product algebra. The connection between the two algebras extends also to the fusion rules.
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.
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.
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.
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.
Renormalization of composite operators in Yang-Mills theories using a general covariant gauge
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.
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2014-05-01
We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the framework of the functional renormalization group. This result follows from our observations: (i) the vanishing imaginary part of the effective average action is realized for arbitrary infrared cutoff as a novel fixed point solution of the flow equation for the complex-valued effective average action and (ii) an approximate analytical solution for the effective average action is obtained without the pure imaginary part for large infrared cutoff. This result suggests that there exists a physical mechanism for maintaining the stability or staying on the fixed point even for sufficiently small infrared cutoff. We argue that dynamical gluon mass generation (related to two-gluon bound states identified with glueballs) occurs due to the Becchi-Rouet-Stora-Tyutin-invariant vacuum condensate of mass dimension two without causing instability.
2D Potential theory using complex functions and conformal mapping
NASA Astrophysics Data System (ADS)
Le Maire, Pauline; Munschy, Marc
2016-04-01
For infinitely horizontally extended bodies, functions that describe potential and field equations (gravity and magnetics) outside bodies are 2D and harmonic. The consequence of this property is that potential and field equations can be written as complex analytic functions. We define these complex functions whose real part is the commonly used real function and imaginary part is its Hilbert transform. Using data or synthetic cases the transformation is easily performed in the Fourier domain by setting to zero all values for negative frequencies. Written as complex functions of the complex variable, equations of potential and field in gravity and magnetics for different kinds of geometries are simple and correspond to powers of the inverse of the distance. For example, it is easily shown that for a tilted dyke, the dip and the apparent inclination have the same effect on the function and consequently that it is not possible, with data, to compute one of both values without knowing the other. Conformal mapping is an original way to display potential field functions. Considering that the complex variable corresponds to the real axis, complex potential field functions resume to a limaçon, a curve formed by the path of the point fixed to a circle when that circle rolls around the outside of another circle. For example, the point corresponding to the maximum distance to the origin of the complex magnetic field due to a cylinder, corresponds to the maximum of the analytic signal as defined by Nabighan in 1972 and its phase corresponds to the apparent inclination. Several applications are shown in different geological contexts using aeromagnetic data.
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.
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.
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.
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.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
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.
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.
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.
The crystal nucleation theory revisited: The case of 2D colloidal crystals
NASA Astrophysics Data System (ADS)
González, A. E.; Ixtlilco-Cortés, L.
2011-03-01
Most of the theories and studies of crystallization and crystal nucleation consider the boundaries between the crystallites and the fluid as smooth. The crystallites are the small clusters of atoms, molecules and/or particles with the symmetry of the crystal lattice that, with a slight chance of success, would grow to form the crystal grains. In fact, in the classical nucleation theory, the crystallites are assumed to have a spherical shape (circular in 2D). As far are we are aware, there is only one experimental work [1] on colloidal crystals that founds rough surfaces for the crystallites and for the crystal grains. Motivated by this work, we performed large Kinetic Monte Carlo simulations in 2D, that would follow the eventual growing of a few crystallites to form the crystal grains. The used potential has, besides the impenetrable hard core, a soft core followed by a potential well. We found that indeed the crystallites have a fractal boundary, whose value we were able to obtain. See the figure below of a typical isolated crystallite. We were also able to obtain the critical crystallite size, measured by its number of particles, Nc, and not by any critical radius. The boundaries of the crystals above Nc also have a fractal structure but of a lower value, closer to one. Finally, we also obtained the line tension between the crystallites and the surrounding fluid, as function of temperature and particle diameter, as well as the chemical potential difference between these two phases. In the URL: www.fis.unam.mx˜˜agus˜ there are posted two movies that can be downloaded: (1) 2D_crystal_nucleation.mp4, and (2) 2D_crystal_growth.mp4, that illustrate the crystal nucleation and its further growth.
Transfer of learning between 2D and 3D sources during infancy: Informing theory and practice
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
Chiral scale and conformal invariance in 2D quantum field theory.
Hofman, Diego M; Strominger, Andrew
2011-10-14
It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Confinement and lattice gauge theory
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.
Ion acoustic wave collapse via two-ion wave decay: 2D Vlasov simulation and theory
NASA Astrophysics Data System (ADS)
Chapman, Thomas; Berger, Richard; Banks, Jeffrey; Brunner, Stephan
2015-11-01
The decay of ion acoustic waves (IAWs) via two-ion wave decay may transfer energy from the electric field of the IAWs to the particles, resulting in a significant heating of resonant particles. This process has previously been shown in numerical simulations to decrease the plasma reflectivity due to stimulated Brillouin scattering. Two-ion wave decay is a fundamental property of ion acoustic waves that occurs over most if not all of the parameter space of relevance to inertial confinement fusion experiments, and can lead to a sudden collapse of IAWs. The treatment of all species kinetically, and in particular the electrons, is required to describe the decay process correctly. We present fully kinetic 2D+2V Vlasov simulations of IAWs undergoing decay to a highly nonlinear turbulent state using the code LOKI. The scaling of the decay rate with characteristic plasma parameters and wave amplitude is shown. A new theory describing two-ion wave decay in 2D, that incorporates key kinetic properties of the electrons, is presented and used to explain quantitatively for the first time the observed decay of IAWs. Work performed under auspices of U.S. DoE by LLNL, Contract DE-AC52-07NA2734. Funded by LDRD 15-ERD-038 and supported by LLNL Grand Challenge allocation.
Electrostatic drift waves in a 2D magnetic current sheet - a new kinetic theory
NASA Astrophysics Data System (ADS)
Fruit, G.; Louarn, P.; Tur, A.
2015-12-01
In the general context of understanding the possible destabilization of the magnetotail before a substorm, a kinetic model for electromagnetic instabilities in resonant interaction with trapped bouncing electrons has been proposed for several years. Fruit et al. 2013 already used it to investigate the possibilities for electrostatic instabilities. Tur et al. 2014 generalizes the model for full electromagnetic perturbations.It turns out that some corrections should be added to the electrostatic version of Fruit et al. 2013. We propose to revist the theory in this present paper.Starting with a modified 2D Harris sheet as equilibrium state, the linearized gyrokinetic Vlasov equation is solved for electrostatic fluctuations with period of the order of the electron bounce period (a few seconds). The particle motion is restricted to its first Fourier component along the magnetic field and this allows the complete time integration of the non local perturbed distribution functions. The dispersion relation for electrostatic modes is finally obtained through the quasineutrality condition.The new feature of the present model is the inclusion of diamagnetic drift effects due to the density gradient in the tail. It is well known in MHD theory that drift waves are driven unstable through collisions or other dissipative effects. Here electrostatic drift waves are revisited in this more complete kinetic model including bouncing electrons and finite Larmor radius effects. A new mode has been found with original propagation proprieties. It is moreover mildly unstable due to electron or ion damping (dissipative instability).
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.
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.
2D-4D correspondence: Towers of kinks versus towers of monopoles in N=2 theories
NASA Astrophysics Data System (ADS)
Bolokhov, Pavel A.; Shifman, Mikhail; Yung, Alexei
2012-04-01
We continue to study the BPS spectrum of the N=(2,2) CPN-1 model with the ZN-symmetric twisted mass terms. We focus on analysis of the “extra” towers found previously in [P. A. Bolokhov, M. Shifman, and A. Yung, arXiv:1104.5241], and compare them to the states that can be identified in the quasiclassical domain. Exact analysis of the strong-coupling states shows that not all of them survive when passing to the weak-coupling domain. Some of the states decay on the curves of the marginal stability. Thus, not all strong-coupling states can be analytically continued to weak coupling to match the observable bound states. At weak coupling, we confirm the existence of bound states of topologically charged kinks and elementary quanta. Quantization of the U(1) kink modulus leads to formation of towers of such states. For the ZN-symmetric twisted masses their number is by far less than N-1 as was conjectured previously. We investigate the quasiclassical limit and show that out of N possible towers only two survive in the spectrum for odd N, and a single tower for even N. In the case of CP2 theory the related curves of the marginal stability are discussed in detail. In these points we overlap and completely agree with the results of Dorey and Petunin. We also comment on 2D-4D correspondence.
Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes
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.
Ramadas, Sivaram N; Jackson, Joseph C; Dziewierz, Jerzy; O'Leary, Richard; Gachagan, Anthony
2014-03-01
Two-dimensional ultrasonic phased arrays are becoming increasingly popular in nondestructive evaluation (NDE). Sparse array element configurations are required to fully exploit the potential benefits of 2-D phased arrays. This paper applies the conformal mapping technique as a means of designing sparse 2-D array layouts for NDE applications. Modeling using both Huygens' field prediction theory and 2-D fast Fourier transformation is employed to study the resulting new structure. A conformal power map was used that, for fixed beam width, was shown in simulations to have a greater contrast than rectangular or random arrays. A prototype aperiodic 2-D array configuration for direct contact operation in steel, with operational frequency ~3 MHz, was designed using the array design principle described in this paper. Experimental results demonstrate a working sparse-array transducer capable of performing volumetric imaging.
A critical review of the research on the extreme male brain theory and digit ratio (2D:4D).
Teatero, Missy L; Netley, Charles
2013-11-01
Boys are more likely than girls to be diagnosed with an autism spectrum disorder (ASD). The extreme male brain (EMB) theory of ASD suggests that fetal testosterone (FT) exposure may underlie sex differences in autistic traits. A link between the organizational effects of FT on the brain and ASD is often drawn based on research using digit ratio (2D:4D), a putative biomarker, without a full survey of the findings. This paper critically and quantitatively reviews the research on the relationship between 2D:4D and ASD as well as autism spectrum, empathizing, and systemizing measures in neurotypical populations. Overall, there is some support for the EMB theory in all four areas, particularly the 2D:4D-ASD relationship. Recommendations for future research are provided.
Raman 2D-band splitting in graphene: theory and experiment.
Frank, Otakar; Mohr, Marcel; Maultzsch, Janina; Thomsen, Christian; Riaz, Ibtsam; Jalil, Rashid; Novoselov, Kostya S; Tsoukleri, Georgia; Parthenios, John; Papagelis, Konstantinos; Kavan, Ladislav; Galiotis, Costas
2011-03-22
We present a systematic experimental and theoretical study of the two-phonon (2D) Raman scattering in graphene under uniaxial tension. The external perturbation unveils that the 2D mode excited with 785 nm has a complex line-shape mainly due to the contribution of two distinct double resonance scattering processes (inner and outer) in the Raman signal. The splitting depends on the direction of the applied strain and the polarization of the incident light. The results give new insight into the nature of the 2D band and have significant implications for the use of graphene as reinforcement in composites since the 2D mode is crucial to assess how effectively graphene uptakes an applied stress or strain.
Character relations and replication identities in 2d Conformal Field Theory
NASA Astrophysics Data System (ADS)
Bantay, P.
2016-10-01
We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in simple cases.
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.
Destabilization of 2D magnetic current sheets by resonance with bouncing electron - a new theory
NASA Astrophysics Data System (ADS)
Fruit, Gabriel; Louarn, Philippe; Tur, Anatoly
2016-07-01
In the general context of understanding the possible destabilization of the magnetotail before a substorm, we propose a kinetic model for electromagnetic instabilities in resonant interaction with trapped bouncing electrons. The geometry is clearly 2D and uses Harris sheet profile. Fruit et al. 2013 already used this model to investigate the possibilities of electrostatic instabilities. Tur et al. 2014 generalizes the model for full electromagnetic perturbations. Starting with a modified Harris sheet as equilibrium state, the linearized gyrokinetic Vlasov equation is solved for electromagnetic fluctuations with period of the order of the electron bounce period (a few seconds). The particle motion is restricted to its first Fourier component along the magnetic field and this allows the complete time integration of the non local perturbed distribution functions. The dispersion relation for electromagnetic modes is finally obtained through the quasi neutrality condition and the Ampere's law for the current density. The present talk will focus on the main results of this theory. The electrostatic version of the model may be applied to the near-Earth environment (8-12 R_{E}) where beta is rather low. It is showed that inclusion of bouncing electron motion may enhance strongly the growth rate of the classical drift wave instability. This model could thus explain the generation of strong parallel electric fields in the ionosphere and the formation of aurora beads with wavelength of a few hundreds of km. In the electromagnetic version, it is found that for mildly stretched current sheet (B_{z} > 0.1 B _{lobes}) undamped modes oscillate at typical electron bounce frequency with wavelength of the order of the plasma sheet thickness. As the stretching of the plasma sheet becomes more intense, the frequency of these normal modes decreases and beyond a certain threshold in B_{z}/B _{lobes}, the mode becomes explosive (pure imaginary frequency) with typical growing rate of a few
Yogurtcu, Osman N.; Johnson, Margaret E.
2015-01-01
The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute
Ultrasonic tissue characterization via 2-D spectrum analysis: theory and in vitro measurements.
Liu, Tian; Lizzi, Frederic L; Ketterling, Jeffrey A; Silverman, Ronald H; Kutcher, Gerald J
2007-03-01
A theoretical model is described for application in ultrasonic tissue characterization using a calibrated 2-D spectrum analysis method. This model relates 2-D spectra computed from ultrasonic backscatter signals to intrinsic physical properties of tissue microstructures, e.g., size, shape, and acoustic impedance. The model is applicable to most clinical diagnostic ultrasound systems. Two experiments employing two types of tissue architectures, spherical and cylindrical scatterers, are conducted using ultrasound with center frequencies of 10 and 40 MHz, respectively. Measurements of a tissue-mimicking phantom with an internal suspension of microscopic glass beads are used to validate the theoretical model. Results from in vitro muscle fibers are presented to further elucidate the utility of 2-D spectrum analysis in ultrasonic tissue characterization.
NASA Astrophysics Data System (ADS)
Ayissi, Raoul Domingo; Noutchegueme, Norbert; Etoua, Remy Magloire; Tchagna, Hugues Paulin Mbeutcha
2015-09-01
Recently in 2005, Briani and Rampazzo (Nonlinear Differ Equ Appl 12:71-91, 2005) gave, using results of Crandall and Lions (Ill J Math 31:665-688, 1987), Ishii (Indiana Univ Math J 33: 721-748, 1984, Bull Fac Sci Eng 28: 33-77, 1985) and Ley (Adv Diff Equ 6:547-576, 2001) a density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians. In this paper we show, using an important result of Briani and Rampazzo (Nonlinear Differ Equ Appl 12:71-91, 2005) the existence and uniqueness of viscosity solutions to the one-body Liouville relativistic equation in Yang-Mills charged Bianchi space times with non-zero mass. To our knowledge, the method used here is original and thus, totally different from those used in Alves (C R Acad Sci Paris Sér A 278:1151-1154, 1975), Choquet-Bruhat and Noutchegueme (C R Acad Sci Paris Sér I 311, 1973), Choquet-Bruhat and Noutchegueme (Ann Inst Henri Poincaré 55:759-787, 1991), Choquet-Bruhat and Noutchegueme (Pitman Res Notes Math Ser 253:52-71, 1992), Noutchegueme and Noundjeu (Ann Inst Henri Poincaré 1:385-404, 2000), Wollman (J Math Anal Appl 127:103-121, 1987) and Choquet-Bruhat (Existence and uniqueness for the Einstein-Maxwell-Liouville system. Volume dedicated to Petrov, Moscow, 1971) who have studied the same equation.
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.
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…
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.
2D-pattern matching image and video compression: theory, algorithms, and experiments.
Alzina, Marc; Szpankowski, Wojciech; Grama, Ananth
2002-01-01
In this paper, we propose a lossy data compression framework based on an approximate two-dimensional (2D) pattern matching (2D-PMC) extension of the Lempel-Ziv (1977, 1978) lossless scheme. This framework forms the basis upon which higher level schemes relying on differential coding, frequency domain techniques, prediction, and other methods can be built. We apply our pattern matching framework to image and video compression and report on theoretical and experimental results. Theoretically, we show that the fixed database model used for video compression leads to suboptimal but computationally efficient performance. The compression ratio of this model is shown to tend to the generalized entropy. For image compression, we use a growing database model for which we provide an approximate analysis. The implementation of 2D-PMC is a challenging problem from the algorithmic point of view. We use a range of techniques and data structures such as k-d trees, generalized run length coding, adaptive arithmetic coding, and variable and adaptive maximum distortion level to achieve good compression ratios at high compression speeds. We demonstrate bit rates in the range of 0.25-0.5 bpp for high-quality images and data rates in the range of 0.15-0.5 Mbps for a baseline video compression scheme that does not use any prediction or interpolation. We also demonstrate that this asymmetric compression scheme is capable of extremely fast decompression making it particularly suitable for networked multimedia applications.
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
NASA Astrophysics Data System (ADS)
Song, Jaewon
2016-02-01
We study superconformal indices of 4d {N}=2 class S theories with certain irregular punctures called type I k,N . This class of theories include generalized Argyres-Douglas theories of type ( A k-1 , A N -1) and more. We conjecture the superconformal indices in certain simplified limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I k,N . We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd N. Fromtheindex,wearguethatcertainshort-multipletwhichcanappearintheOPEof the stress-energy tensor is absent in the ( A 1 , A 2 n ) theory. We also discuss the mixed Schur indices for the {N}=1 class {S} theories with irregular punctures.
Galvao, C.A.; Nutku, Y.
1996-12-01
mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}
Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.
Spencer, Austin P; Li, Hebin; Cundiff, Steven T; Jonas, David M
2015-04-30
A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.
Truncated conformal space approach for 2D Landau–Ginzburg theories
Coser, A.; Beria, M.; Brandino, G. P.; ...
2014-12-10
In this study, We examine the spectrum of Landau–Ginzburg theories in 1 + 1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a Φ² theory (i.e. a free massive boson) in this framework. We then turn to Φ⁴ in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of Φ⁴ where kink excitations together with their bound states are present.more » We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of Φ⁶ Landau-Ginzburg theory, again finding agreement.« less
Truncated conformal space approach for 2D Landau–Ginzburg theories
Coser, A.; Beria, M.; Brandino, G. P.; Konik, R. M.; Mussardo, G.
2014-12-10
In this study, We examine the spectrum of Landau–Ginzburg theories in 1 + 1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a Φ² theory (i.e. a free massive boson) in this framework. We then turn to Φ⁴ in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of Φ⁴ where kink excitations together with their bound states are present. We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of Φ⁶ Landau-Ginzburg theory, again finding agreement.
Theory and operation of 2-D array piezoelectric micromachined ultrasound transducers.
Dausch, David E; Castellucci, John B; Chou, Derrick R; von Ramm, Olaf T
2008-11-01
Piezoelectric micromachined ultrasound transducers (pMUTs) are a new approach for the construction of 2-D arrays for forward-looking 3-D intravascular (IVUS) and intracardiac (ICE) imaging. Two-dimensional pMUT test arrays containing 25 elements (5 x 5 arrays) were bulk micromachined in silicon substrates. The devices consisted of lead zirconate titanate (PZT) thin film membranes formed by deep reactive ion etching of the silicon substrate. Element widths ranged from 50 to 200 microm with pitch from 100 to 300 mum. Acoustic transmit properties were measured in de-ionized water with a calibrated hydrophone placed at a range of 20 mm. Measured transmit frequencies for the pMUT elements ranged from 4 to 13 MHz, and mode of vibration differed for the various element sizes. Element capacitance varied from 30 to over 400 pF depending on element size and PZT thickness. Smaller element sizes generally produced higher acoustic transmit output as well as higher frequency than larger elements. Thicker PZT layers also produced higher transmit output per unit electric field applied. Due to flexure mode operation above the PZT coercive voltage, transmit output increased nonlinearly with increased drive voltage. The pMUT arrays were attached directly to the Duke University T5 Phased Array Scanner to produce real-time pulse-echo B-mode images with the 2-D pMUT arrays.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Renormalization constants from string theory.
NASA Astrophysics Data System (ADS)
di Vecchia, P.; Magnea, L.; Lerda, A.; Russo, R.; Marotta, R.
The authors review some recent results on the calculation of renormalization constants in Yang-Mills theory using open bosonic strings. The technology of string amplitudes, supplemented with an appropriate continuation off the mass shell, can be used to compute the ultraviolet divergences of dimensionally regularized gauge theories. The results show that the infinite tension limit of string amplitudes corresponds to the background field method in field theory.
NASA Astrophysics Data System (ADS)
Brandt, Bastian B.; Lohmayer, Robert; Wettig, Tilo
2016-11-01
We explore an alternative discretization of continuum SU( N c ) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N b can be as small as N c . In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U( N c ) to SU( N c ), (ii) derive refined bounds on N b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
Song, Jaewon
2016-02-05
We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type Ik,N. This class of theories include generalized Argyres-Douglas theories of type (Ak-1, AN-1) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture Ik,N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index formore » odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A1,A2n) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.« less
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
Song, Jaewon
2016-02-05
We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type I_{k,N}. This class of theories include generalized Argyres-Douglas theories of type (A_{k-1}, A_{N-1}) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I_{k,N}. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A_{1},A_{2n}) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.
On extended analytic theory of 2D ballooning modes in tokamak plasmas
NASA Astrophysics Data System (ADS)
Abdoul, Peshwaz; Dickinson, David; Roach, Colin; Wilson, Howard
2016-10-01
We have extended the leading order ballooning theory which typically yields more unstable isolated mode (IM) that usually sit on the outboard mid-plane, to higher order where less unstable general mode (GM) sits at a different poloidal location. Our analytic theory has revealed that any poloidal shift of the mode with respect to the outboard mid-plane - arising from the effect of profile variations, for example - is always accompanied by an asymmetry of the radial eigenmode structure. Hence, GMs have radial asymmetry. Our theory can have important consequences, especially for calculations that invoke quasilinear theory to model intrinsic rotation arising from Reynolds stress. This is very important in ITER for which external torques are small. In such theories it is the radial asymmetry in the global GM mode which can generate a Reynolds stress that could in principle contribute to the poloidal flow during the low to high (L-H) mode transition in tokamaks. I am also an associate member at the York Plasma Institute, University of York and teaching at the Physics Department, University of Sulaimani, Kurdistan Region, Iraq.
Analytic theory for the selection of 2-D needle crystal at arbitrary Peclet number
NASA Technical Reports Server (NTRS)
Tanveer, Saleh
1989-01-01
An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.
A comprehensive 2-D divertor data set from DIII-D for edge theory validation
Fenstermacher, M.E.; Allen, S.L.; Hill, D.N.
1996-02-01
A comprehensive set of experiments has been carried out on the DIII-D tokamak to measure the 2-D (R,Z) structure of the divertor plasma in a systematic way using new diagnostics. Measurements cover the divertor radially from inside the X-point to the outer target plate and vertically from the target plate to above the X-point. Identical, repeatable shots were made, each having radial sweeps of the X-point and divertor strike points, to allow complete plasma and radiation profile measurements. Data have been obtained in ohmic, L-mode, ELMing H-mode, and reversed B{sub T} operation ({gradient}B drift away from the X-point). In addition, complete measurements were made of radiative divertor plasmas with a Partially Detached Divertor (PDD) induced by D{sub 2} injection and with a Radiating Mantle induced by Impurity injection (RMI) using neon and nitrogen. The data set includes first observations of the radial and poloidal profiles of the X-point, inner and outer leg plasmas in PDD and RMI radiative divertor operation. Preliminary data analysis shows that intrinsic impurities play a critical role in determining the SOL and divertor conditions.
Noncommutative topological theories of gravity
NASA Astrophysics Data System (ADS)
García-Compeán, H.; Obregón, O.; Ramírez, C.; Sabido, M.
2003-08-01
The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. Finally, we speculate on the description of noncommutative gravitational instantons, as well as noncommutative local gravitational anomalies.
Black holes in the Einstein-Gauss-Bonnet theory and the geometry of their thermodynamics—II
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata; Chakraborty, Subenoy
2010-03-01
In the present work we study (i) the charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as the Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory
Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun
2010-09-15
We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.
Gauge theory of defects in continuous media I
NASA Astrophysics Data System (ADS)
Sahoo, D.
2006-11-01
We present a selective review of the gauge theory of defects in the elastic continuum. After introducing the essential geometric concepts of continuum mechanics in the presence of defects, the classical defect dynamics equations involving dislocation and disclination density tensors are introduced. The mathematical structure of gauge theories is briefly discussed. Typical recent works covering Yang-Mills type gauge theories and gravity type gauge theories are touched upon in a qualitative way.
Coupled leaky mode theory for light absorption in 2D, 1D, and 0D semiconductor nanostructures.
Yu, Yiling; Cao, Linyou
2012-06-18
We present an intuitive, simple theoretical model, coupled leaky mode theory (CLMT), to analyze the light absorption of 2D, 1D, and 0D semiconductor nanostructures. This model correlates the light absorption of nanostructures to the optical coupling between incident light and leaky modes of the nanostructure. Unlike conventional methods such as Mie theory that requests specific physical features of nanostructures to evaluate the absorption, the CLMT model provides an unprecedented capability to analyze the absorption using eigen values of the leaky modes. Because the eigenvalue shows very mild dependence on the physical features of nanostructures, we can generally apply one set of eigenvalues calculated using a real, constant refractive index to calculations for the absorption of various nanostructures with different sizes, different materials, and wavelength-dependent complex refractive index. This CLMT model is general, simple, yet reasonably accurate, and offers new intuitive physical insights that the light absorption of nanostructures is governed by the coupling efficiency between incident light and leaky modes of the structure.
NASA Astrophysics Data System (ADS)
Ma, ShengQian; Li, Feng; Geng, JiGuo
2017-04-01
Since efficient synthesis of C2N holey two-dimensional (h2D) crystal has been possible, bandgap modulation through use of analogous nanoribbon and nanotube structures has attracted strong interest. In this study, bandgap modulation of Si2N-h2D nanoribbons and nanotubes under elastic strain has been deeply researched using density functional theory calculations. The results indicate that the bandgap of Si2N-h2D nanoribbons and nanotubes in zigzag and armchair configurations can be tuned in both directions, namely by stretching or compressing, in the range of ɛ = ( d - d 0)/ d 0 from -10% to 10%. It is also found that the bandgap of Si2N-h2D nanoribbons and nanotubes varies with their width. Therefore, it is predicted that Si2N-h2D nanoribbons and nanotubes have great potential for application in nanoscale strain sensors and optoelectronics.
Modified coupling procedure for the Poincare gauge theory of gravity
Kazmierczak, Marcin
2009-06-15
The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincare gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.
Perturbative quantum gravity as a double copy of gauge theory.
Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik
2010-08-06
In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
New phase transitions in Chern-Simons matter theory
NASA Astrophysics Data System (ADS)
Zahabi, Ali
2016-02-01
Applying the machinery of random matrix theory and Toeplitz determinants we study the level k, U (N) Chern-Simons theory coupled with fundamental matter on S2 ×S1 at finite temperature T. This theory admits a discrete matrix integral representation, i.e. a unitary discrete matrix model of two-dimensional Yang-Mills theory. In this study, the effective partition function and phase structure of the Chern-Simons matter theory, in a special case with an effective potential namely the Gross-Witten-Wadia potential, are investigated. We obtain an exact expression for the partition function of the Chern-Simons matter theory as a function of k, N, T, for finite values and in the asymptotic regime. In the Gross-Witten-Wadia case, we show that ratio of the Chern-Simons matter partition function and the continuous two-dimensional Yang-Mills partition function, in the asymptotic regime, is the Tracy-Widom distribution. Consequently, using the explicit results for free energy of the theory, new second-order and third-order phase transitions are observed. Depending on the phase, in the asymptotic regime, Chern-Simons matter theory is represented either by a continuous or discrete two-dimensional Yang-Mills theory, separated by a third-order domain wall.
NASA Astrophysics Data System (ADS)
Shifman, M.
Asymptotic freedom as the basic property of QCD was discovered by Gross, Wilczek, and Politzer in 1973. Personal recollections of David Gross which are being published in this Volume vividly describe the historical background and the chain of events which led to this fundamental breakthrough. Unfortunately, I failed to obtain Politzer's side of the story. Some details can be found in an interview which Prof. Politzer gave to R. Crease and C. Mann on February 21, 1985. Below I acquaint the reader with the pre-1973 appearances of asymptotic freedom which, unfortunately, were not recognized.
Plasmon mass scale in classical nonequilibrium gauge theory
NASA Astrophysics Data System (ADS)
Lappi, T.; Peuron, J.
2017-01-01
Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real-time Yang-Mills theory on a lattice in three spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and the measurement of oscillations between electric and magnetic field modes after artificially introducing a homogeneous color electric field. We find that a version of the dispersion relation that uses electric fields and their time derivatives agrees with the other methods within 50%.
NASA Astrophysics Data System (ADS)
Leever, Karen; Oncken, Onno; Thorden Haug, Øystein
2015-04-01
For 2D critical taper theory to be applicable to 3D natural cases, cylindric deformation is a requirement. The assumption of cylindricity is violated in case of localized perturbations (subducting seamount, localized sedimentation) or due to a lateral change in decollement strength or depth. In natural accretionary wedges and fold-and-thrust belts, along strike changes may occur in a variety of ways: geometrical (due to a protruding indenter or a change in decollement depth), through a lateral change in basal friction (leading to laterally different tapers), or through a change in surface slope (by strongly localized fan sedimentation on accretionary wedges). Recent numerical modelling results (Ruh et al., 2013) have shown that lateral coupling preferentially occurs for relatively small perturbations, i.e. the horizontal shear stress caused by the perturbation is supported by the system. Lateral linking of the wedge in front of a protruding indenter to the wedge in front of the trailing edge of the back stop leads to curved thrust fronts and importantly it has been noted that even outside the curved zone, where the wedge front is again parallel to the direction of tectonic transport, the lateral effect is still evident: both tapers are different from the analytical prediction. We present results from a 3D analogue modelling parameter study to investigate this behavior more quantitatively, with the objective of empirically finding a lateral length scale of deformation in brittle contractional wedges. For a given wedge strength (angle of internal friction), we infer this to be a function of the size (width) of the perturbation and its magnitude (difference in basal friction). To this end we run different series of models in which we systematically vary the width and/or magnitude of a local perturbation. In the first series, the width of a zone of high basal friction is varied, in the second series we vary the width of an indenter and in the third series
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.
NASA Astrophysics Data System (ADS)
Chiodaroli, M.; Günaydin, M.; Johansson, H.; Roiban, R.
2016-07-01
We show that scattering amplitudes in magical, symmetric or homogeneous N =2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color-kinematics duality. The left-hand copy is N =2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the right-hand copy is a nonsupersymmetric theory that can be identified as the dimensional reduction of a D -dimensional Yang-Mills theory coupled to P fermions. For generic D and P , the double copy gives homogeneous supergravities. For P =1 and D =7 , 8, 10, 14, it gives the magical supergravities. We compute explicit amplitudes, discuss their soft limits, and study the UV behavior at one loop.
Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-11
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
NASA Astrophysics Data System (ADS)
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
Bern, Z.; Boucher-Veronneau, C.; Johansson, H.; /Saclay
2011-08-19
We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N {ge} 4 supergravity and the corresponding (super-)Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories.
Dualities, CPT symmetry and dimensional reduction in string theory
NASA Astrophysics Data System (ADS)
Bertolami, O.
1997-08-01
In this lecture we address the following issues in the context of string theories: i) The role played by S and T dualities in obtaining topological inflation in N=1 supergravity models, ii) A mechanism for generating the baryon asymmetry of the universe based on the string interactions that violate CPT symmetry and iii) The quantum cosmology of the dimensionally reduced multidimensional Einstein-Yang-Mills system.
New set of 2D/3D thermodynamic indices for proteins. A formalism based on “ Molten Globule” theory
NASA Astrophysics Data System (ADS)
Ruiz-Blanco Yasser, B.; García, Y.; Sotomayor-Torres, C. M.; Yovani, Marrero-Ponce
We define eight new macromolecular indices, and several related descriptors for proteins. The coarse grained methodology used for its deduction ensures its fast execution and becomes a powerful potential tool to explore large databases of protein structures. The indices are intended for stability studies, predicting Φ-values, predicting folding rate constants, protein QSAR/QSPR as well as protein alignment studies. Also, these indices could be used as scoring function in protein-protein docking or 3D protein structure prediction algorithms and any others applications which need a numerical code for proteins and/or residues from 2D or 3D format.
Dyson-Schwinger Approach to Strongly Coupled Theories
NASA Astrophysics Data System (ADS)
Popovici, Carina
2013-03-01
Although non-perturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body systems. In this paper, we aim to provide a modest overview on a few notable applications of Dyson-Schwinger equations to QCD and condensed matter physics. After a short introduction, we lay out some formal considerations and proceed by addressing the confinement problem. We discuss in some detail the heavy quark limit of Coulomb gauge QCD, in particular the simple connection between the non-perturbative Green's functions of Yang-Mills theory and the confinement potential. Landau gauge results on the infrared Yang-Mills propagators are also briefly reviewed. We then focus on less common applications, in graphene and high-temperature superconductivity. We discuss recent developments, and present theoretical predictions that are supported by experimental findings.
Overview of K-Theory Applied to Strings
NASA Astrophysics Data System (ADS)
Witten, Edward
2001-04-01
K-theory provides a framework for classifying Ramond-Ramond (RR) charges and fields.K-theory of manifolds has a natural extension to K-theory of noncommutative algebras, such as the algebras considered in noncommutative Yang-Mills theory or in open string field theory. In a number of concrete problems, the K-theory analysis proceeds most naturally if one starts out with an infinite set of D-branes, reduced by tachyon condensation to a finite set. This suggests that string field theory should be reconsidered for N = ∞.
A Critical Review of the Research on the Extreme Male Brain Theory and Digit Ratio (2D:4D)
ERIC Educational Resources Information Center
Teatero, Missy L.; Netley, Charles
2013-01-01
Boys are more likely than girls to be diagnosed with an autism spectrum disorder (ASD). The extreme male brain (EMB) theory of ASD suggests that fetal testosterone (FT) exposure may underlie sex differences in autistic traits. A link between the organizational effects of FT on the brain and ASD is often drawn based on research using digit ratio…
NASA Technical Reports Server (NTRS)
Hanson, Donald B.
1994-01-01
A two dimensional linear aeroacoustic theory for rotor/stator interaction with unsteady coupling was derived and explored in Volume 1 of this report. Computer program CUP2D has been written in FORTRAN embodying the theoretical equations. This volume (Volume 2) describes the structure of the code, installation and running, preparation of the input file, and interpretation of the output. A sample case is provided with printouts of the input and output. The source code is included with comments linking it closely to the theoretical equations in Volume 1.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
NASA Astrophysics Data System (ADS)
Harrell, S. D.; She, C.; Krueger, D. A.; Yuan, T.; Reising, S. C.
2008-12-01
The Chapman mechanism (1939) offers the accepted chemical pathway for the production of excited states of mesospheric sodium, leading to nightglow at two wavelengths: D2 (589.158 nm) and D1 (589.756 nm). While the Chapman mechanism leaves open the possibility that the intensity ratio of the two transitions may vary due to the chemical reaction involving atomic oxygen, early observations by Sipler and Biondi (1978) yielded the value of two within experimental error. Recent work by Slanger et al. (2005), however, showed that not only does the intensity ratio vary, but its value is related to the concentration ratio of atomic oxygen [O] to molecular oxygen [O2]. They proposed a modification of the Chapman mechanism involving two competing chemical pathways for sodium production to account for the observed variation. This paper will describe our compact, Faraday filter-based spectrometer to measure the D2/D1 intensity ratio of the sodium nightglow from the upper mesosphere. The novelty of this method also permits determination of the fractional contributions of the two chemical pathways to test the validity of the modified Chapman mechanism for Na chemistry, as well as to infer information about [O]/[O2]. Since the delineation between the two chemical pathways requires a spectral resolution of 0.0002 nm, this is not possible with any other existing instrument. With this spectrometer deployed at the Colorado State University sodium lidar facility (41°N, 105°W), we expect to be able to measure short-term variations of the sodium nightglow intensity ratio and the chemical pathway fraction, from which [O]/[O2] can be inferred. These observations may yield new insights into mesospheric chemistry, especially for atomic and molecular oxygen, which play a key role in upper atmospheric chemistry and dynamics.
Osp(1{vert_bar}2) Chern-Simons gauge theory as 2D N=1 induced supergravity
Ezawa, K.; Ishikawa, A.
1997-08-01
We demonstrate the close relationship between Chern-Simons gauge theory with the gauge group Osp(1{vert_bar}2) and N=1 induced supergravity in two dimensions. More precisely, the inner product of the physical states in the former yields the partition function of the latter evaluated in the Wess-Zumino supergauge. It is also shown that the moduli space of flat Osp(1{vert_bar}2) connections naturally includes a super Teichm{umlt u}ller space of super Riemann surfaces. {copyright} {ital 1997} {ital The American Physical Society}
Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia
2016-03-14
We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.
Gauge theory of fermions on R X S{sup 3} spacetime
Dariescu, M.A.; Dariescu, C.; Gottlieb, I.
1995-06-01
A Lorentz-invariant gauge theory for massive fermions on R X S{sup 3} spacetime is built up. Using the symmetry of S{sup 3}, the authors obtain Dirac-type equations and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, they obtain the set of Dirac-Yang-Mills equations on R X S{sup 3} spacetime, pointing out major differences from the Minkowskian case.
Entanglement in weakly coupled lattice gauge theories
NASA Astrophysics Data System (ADS)
Radičević, Ðorđe
2016-04-01
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group G contains a generic logarithmic term at sufficiently weak coupling e. In two spatial dimensions, for a region of linear size r, this term equals 1/2 dim( G) log( e 2 r) and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.
Local renormalizable gauge theories from nonlocal operators
Capri, M.A.L. Lemes, V.E.R. Sobreiro, R.F. Sorella, S.P. Thibes, R.
2008-03-15
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator Tr{integral}A{sub {mu}}1/(D{sup 2}) A{sub {mu}} is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.
Holomorphic field realization of SH c and quantum geometry of quiver gauge theories
NASA Astrophysics Data System (ADS)
Bourgine, Jean-Emile; Matsuo, Yutaka; Zhang, Hong
2016-04-01
In the context of 4D/2D dualities, SH c algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N=2 supersymmetricgaugetheories. Inthispaper,werewritetheSH c algebrainterms of three holomorphic fields D 0( z), D ±1( z) with which the algebra and its representations are simplified. The instanton partition functions for arbitrary N=2 super Yang-Mills theories with A n and A n (1) type quiver diagrams are compactly expressed as a product of four building blocks, Gaiotto state, dilatation, flavor vertex operator and intertwiner which are written in terms of SH c and the orthogonal basis introduced by Alba, Fateev, Litvinov and Tarnopolskiy. These building blocks are characterized by new conditions which generalize the known ones on the Gaiotto state and the Carlsson-Okounkov vertex. Consistency conditions of the inner product give algebraic relations for the chiral ring generating functions defined by Nekrasov, Pestun and Shatashvili. In particular we show the polynomiality of the qq-characters which have been introduced as a deformation of the Yangian characters. These relations define a second quantization of the Seiberg-Witten geometry, and, accordingly, reduce to a Baxter TQ-equation in the Nekrasov-Shatashvili limit of the Omega-background.
Field Theories from the Relativistic Law of Motion
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Dadhich, Naresh
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which could be the Abelian Maxwell electrodynamics or the non-Abelian Yang-Mills theory. On the other hand, the quadratic law demands space-time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tensor theory of gravitational field - general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.
Burton, Julien; Petit, Joachim; Danloy, Emeric; Maggiora, Gerald M; Vercauteren, Daniel P
2013-07-01
Early prediction of ADME properties such as the cytochrome P450 (CYP) mediated drug-drug interactions is an important challenge in the drug discovery area. In this study, we propose to couple an original data mining approach based on Rough Set Theory (RST) to a structural description of molecules. The latter was achieved by using two types of structural keys: (1) the MACCS keys and (2) a set of five in-house fingerprints based on properties of the electron density distributions of chemical groups. The compounds considered are involved in the inhibition of CYP1A2 and CYP2D6. RST allowed the extraction of rules further used as classifiers to predict the inhibitory profile of an independent set of molecules. The results reached prediction accuracies of 90.6 and 88.2 % for CYP1A2 and CYP2D6, respectively. In addition, these classifiers were analyzed to determine which structural fragments were most used for building the rules, revealing relationships between the occurrence of particular molecular fragments and CYP inhibition. The results assessed RST as a suitable tool to build strongly predictive models and infer structure-activity rules associated with potency.
Valla, Jeffrey; Ceci, Stephen J.
2011-01-01
Brain organization theory posits a cascade of physiological and behavioral changes initiated and shaped by prenatal hormones. Recently, this theory has been associated with outcomes including gendered toy preference, 2D/4D digit ratio, personality characteristics, sexual orientation, and cognitive profile (spatial, verbal, and mathematical abilities). We examine the evidence for this claim, focusing on 2D/4D and its putative role as a biomarker for organizational features that influence cognitive abilities/interests predisposing males toward mathematically and spatially intensive careers. Although massive support exists for early brain organization theory overall, there are myriad inconsistencies, alternative explanations, and outright contradictions that must be addressed while still taking the entire theory into account. Like a fractal within the larger theory, the 2D/4D hypothesis mirrors this overall support on a smaller scale while likewise suffering from inconsistencies (positive, negative, and sex-dependent correlations), alternative explanations (2D/4D related to spatial preferences rather than abilities per se), and contradictions (feminine 2D/4D in men associated with higher spatial ability). Using the debate over brain organization theory as the theoretical stage, we focus on 2D/4D evidence as an increasingly important player on this stage, a demonstrative case in point of the evidential complexities of the broader debate, and an increasingly important topic in its own right. PMID:22164187
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
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.
Saririan, Kamran
1997-05-01
In this thesis, the author presents some works in the direction of studying quantum effects in locally supersymmetric effective field theories that appear in the low energy limit of superstring theory. After reviewing the Kaehler covariant formulation of supergravity, he shows the 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. He then presents the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. He also considers the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified. He studies gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, the author includes in the Kaehler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furthermore, a new running behavior of the dilaton arises which he attributes to S-duality. He also discusses the effects of the intermediate scale, and possible phenomenological implications of this model.
NASA Technical Reports Server (NTRS)
Pindera, Marek-Jerzy; Aboudi, Jacob
2000-01-01
The objective of this two-year project was to develop and deliver to the NASA-Glenn Research Center a two-dimensional higher-order theory, and related computer codes, for the analysis and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, brisk blades). To satisfy this objective, two-dimensional version of the higher-order theory, HOTCFGM-2D, and four computer codes based on this theory, for the analysis and design of structural components functionally graded in the radial and circumferential directions were developed in the cylindrical coordinate system r-Theta-z. This version of the higher-order theory is a significant generalization of the one-dimensional theory, HOTCFGM-1D, developed during the FY97 for the analysis and design of cylindrical structural components with radially graded microstructures. The generalized theory is applicable to thin multi-phased composite shells/cylinders subjected to steady-state thermomechanical, transient thermal and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial direction, and arbitrarily distributed in the radial and circumferential direction, thereby allowing functional grading of the internal reinforcement in the r-Theta plane. The four computer codes fgmc3dq.cylindrical.f, fgmp3dq.cylindrical.f, fgmgvips3dq.cylindrical.f, and fgmc3dq.cylindrical.transient.f are research-oriented codes for investigating the effect of functionally graded architectures, as well as the properties of the multi-phase reinforcement, in thin shells subjected to thermomechanical and inertial loading, on the internal temperature, stress and (inelastic) strain fields. The reinforcement distribution in the radial and circumferential directions is specified by the user. The thermal
Field theory on R×S 3 topology. V: SU 2 gauge theory
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-02-01
A gauge theory on R×S 3 topology is developed. It is a generalization to the previously obtained field theory on R×S 3 topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences between them are discussed.
Sokolowsky, Kathleen P; Bailey, Heather E; Hoffman, David J; Andersen, Hans C; Fayer, Michael D
2016-07-21
Two-dimensional infrared (2D IR) data are presented for a vibrational probe in three nematogens: 4-cyano-4'-pentylbiphenyl, 4-cyano-4'-octylbiphenyl, and 4-(trans-4-amylcyclohexyl)-benzonitrile. The spectral diffusion time constants in all three liquids in the isotropic phase are proportional to [T*/(T - T*)](1/2), where T* is 0.5-1 K below the isotropic-nematic phase transition temperature (TNI). Rescaling to a reduced temperature shows that the decays of the frequency-frequency correlation function (FFCF) for all three nematogens fall on the same curve, suggesting a universal dynamic behavior of nematogens above TNI. Spectral diffusion is complete before significant orientational relaxation in the liquid, as measured by optically heterodyne detected-optical Kerr effect (OHD-OKE) spectroscopy, and before any significant orientational randomization of the probe measured by polarization selective IR pump-probe experiments. To interpret the OHD-OKE and FFCF data, we constructed a mode coupling theory (MCT) schematic model for the relationships among three correlation functions: ϕ1, a correlator for large wave vector density fluctuations; ϕ2, the orientational correlation function whose time derivative is the observable in the OHD-OKE experiment; and ϕ3, the FFCF for the 2D IR experiment. The equations for ϕ1 and ϕ2 match those in the previous MCT schematic model for nematogens, and ϕ3 is coupled to the first two correlators in a straightforward manner. Resulting models fit the data very well. Across liquid crystals, the temperature dependences of the coupling constants show consistent, nonmonotonic behavior. A remarkable change in coupling occurs at ∼5 K above TNI, precisely where the rate of spectral diffusion in 5CB was observed to deviate from that of a similar nonmesogenic liquid.
Large N phase transitions in massive N = 2 gauge theories
Russo, J. G.
2014-07-23
Using exact results obtained from localization on S{sup 4}, we explore the large N limit of N = 2 super Yang-Mills theories with massive matter multiplets. In this talk we discuss two cases: N = 2* theory, describing a massive hypermultiplet in the adjoint representation, and super QCD with massive quarks. When the radius of the four-sphere is sent to infinity these theories are described by solvable matrix models, which exhibit a number of interesting phenomena including quantum phase transitions at finite 't Hooft coupling.
Massless fermions and Kaluza--Klein theory with torsion
Wu, Y.; Zee, A.
1984-09-01
A pure Kaluza--Klein theory contains no massless fermion in four-dimensional theory. We investigate the effect of introducing torsion on the internal manifold and find that there are massless fermions. The hope is that given an isometry group the representation to which these fermions belong is fixed, in contrast to the situation in Yang--Mills theory. We show that this is indeed the case, but the representations do not appear to be the ones favored by current theoretical prejudice. The cases with parallelizable torsions on a group manifold as the internal manifold are analyzed in detail.
The Seiberg-Witten map for noncommutative gauge theories
Cerchiai, B.L.; Pasqua, A.F.; Zumino, B.
2002-06-26
The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
Gravity as the square of gauge theory
Bern, Zvi; Dennen, Tristan; Huang Yutin; Kiermaier, Michael
2010-09-15
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen, and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By ''squaring'' the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
Wang, Tuo; Yang, Hui; Kubicki, James D; Hong, Mei
2016-06-13
The native cellulose of bacterial, algal, and animal origins has been well studied structurally using X-ray and neutron diffraction and solid-state NMR spectroscopy, and is known to consist of varying proportions of two allomorphs, Iα and Iβ, which differ in hydrogen bonding, chain packing, and local conformation. In comparison, cellulose structure in plant primary cell walls is much less understood because plant cellulose has lower crystallinity and extensive interactions with matrix polysaccharides. Here we have combined two-dimensional magic-angle-spinning (MAS) solid-state nuclear magnetic resonance (solid-state NMR) spectroscopy at high magnetic fields with density functional theory (DFT) calculations to obtain detailed information about the structural polymorphism and spatial distributions of plant primary-wall cellulose. 2D (13)C-(13)C correlation spectra of uniformly (13)C-labeled cell walls of several model plants resolved seven sets of cellulose chemical shifts. Among these, five sets (denoted a-e) belong to cellulose in the interior of the microfibril while two sets (f and g) can be assigned to surface cellulose. Importantly, most of the interior cellulose (13)C chemical shifts differ significantly from the (13)C chemical shifts of the Iα and Iβ allomorphs, indicating that plant primary-wall cellulose has different conformations, packing, and hydrogen bonding from celluloses of other organisms. 2D (13)C-(13)C correlation experiments with long mixing times and with water polarization transfer revealed the spatial distributions and matrix-polysaccharide interactions of these cellulose structures. Celluloses f and g are well mixed chains on the microfibril surface, celluloses a and b are interior chains that are in molecular contact with the surface chains, while cellulose c resides in the core of the microfibril, outside spin diffusion contact with the surface. Interestingly, cellulose d, whose chemical shifts differ most significantly from those of
Wang, Tuo; Yang, Hui; Kubicki, James D.; Hong, Mei
2017-01-01
The native cellulose of bacterial, algal, and animal origins has been well studied structurally using X-ray and neutron diffraction and solid-state NMR spectroscopy, and is known to consist of varying proportions of two allomorphs, Iα and Iβ, which differ in hydrogen bonding, chain packing, and local conformation. In comparison, cellulose structure in plant primary cell walls is much less understood because plant cellulose has lower crystallinity and extensive interactions with matrix polysaccharides. Here we have combined two-dimensional magic-angle-spinning (MAS) solid-state nuclear magnetic resonance (solid-state NMR) spectroscopy at high magnetic fields with density functional theory (DFT) calculations to obtain detailed information about the structural polymorphism and spatial distributions of plant primary-wall cellulose. 2D 13C-13C correlation spectra of uniformly 13C-labeled cell walls of several model plants resolved seven sets of cellulose chemical shifts. Among these, five sets (denoted a-e) belong to cellulose in the interior of the microfibril while two sets (f and g) can be assigned to surface cellulose. Importantly, most of the interior cellulose 13C chemical shifts differ significantly from the 13C chemical shifts of the Iα and Iβ allomorphs, indicating that plant primary-wall cellulose has different conformations, packing and hydrogen bonding from celluloses of other organisms. 2D 13C-13C correlation experiments with long mixing times and with water polarization transfer revealed the spatial distributions and matrix-polysaccharide interactions of these cellulose structures. Cellulose f and g are well mixed chains on the microfibril surface, cellulose a and b are interior chains that are in molecular contact with the surface chains, while cellulose c resides in the core of the microfibril, outside spin diffusion contact with the surface. Interestingly, cellulose d, whose chemical shifts differ most significantly from those of bacterial, algal
Gauge Theories of Vector Particles
DOE R&D Accomplishments Database
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Kolkoori, Sanjeevareddy; Chitti Venkata, Krishnamurthy; Balasubramaniam, Krishnan
2015-01-01
This article presents an analytical approach for simulation of ultrasonic diffracted wave signals from cracks in two-dimensional geometries based on a novel Huygens-Fresnel Diffraction Model (HFDM). The model employs the frequency domain far-field displacement expressions derived by Miller and Pursey in 2D for a line source located on the free surface boundary of a semi-infinite elastic medium. At each frequency in the bandwidth of a pulsed excitation, the complex diffracted field is obtained by summation of displacements due to the unblocked virtual sources located in the section containing a vertical crack. The time-domain diffracted wave signal amplitudes in a general isotropic solid are obtained by standard Fast Fourier Transform (FFT) procedures. The wedge based finite aperture transducer refracted beam profiles were modelled by treating the finite dimension transducer as an array of line sources. The proposed model is able to evaluate back-wall signal amplitude and lateral wave signal amplitude, quantitatively. The model predicted range-dependent diffracted amplitudes from the edge of a bottom surface-breaking crack in the isotropic steel specimen were compared with Geometrical Theory of Diffraction (GTD) results. The good agreement confirms the validity of the HFDM method. The simulated ultrasonic time-of-flight diffraction (TOFD) A-scan signals for surface-breaking crack lengths 2 mm and 4 mm in a 10 mm thick aluminium specimen were compared quantitatively with the experimental results. Finally, important applications of HFDM method to the ultrasonic quantitative non-destructive evaluation are discussed.
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Roiban, Radu; Volovich, Anastasia
2004-09-24
It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.
Time-Dependent Variational Approach to the pure Gauge Theory for Evaluating the Shear Viscosity
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Lee, Tong-Gyu; Ishii, Hiroshi
2009-10-01
The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schr"odinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the shear viscosity, which is one of the transport coefficients for the pure gluonic matter, by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Hadronic density of states from string theory.
Pando Zayas, Leopoldo A; Vaman, Diana
2003-09-12
We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.
Georgi, Howard; Kats, Yevgeny
2008-09-26
We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale-invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles.
Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
NASA Astrophysics Data System (ADS)
Abe, Hiroyuki; Kobayashi, Tatsuo; Ohki, Hiroshi; Sumita, Keigo; Tatsuta, Yoshiyuki
2014-06-01
We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.
Generalized Lorentz-Dirac equation for a strongly coupled gauge theory.
Chernicoff, Mariano; García, J Antonio; Güijosa, Alberto
2009-06-19
We derive a semiclassical equation of motion for a "composite" quark in strongly coupled large-N_{c} N = 4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Hitchin’s equations and M-theory phenomenology
NASA Astrophysics Data System (ADS)
Pantev, Tony; Wijnholt, Martijn
2011-07-01
Phenomenological compactifications of M-theory involve seven-manifolds with G2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills theory on a three-manifold Q3. We give a general discussion of compactifications of 7d Yang-Mills theory in terms of Higgs bundles on Q3. We show that they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T∗Q3. We explain the dictionary with ALE fibrations over Q3 and conjecture that these configurations have G2 holonomy. We further develop tools to study the low energy effective theory of such a model. We show that the naive massless spectrum is corrected by instanton effects. Taking the instanton effects into account, we find that the massless spectrum and many of the interactions can be computed with Morse theoretic methods.
NASA Astrophysics Data System (ADS)
Engheta, Nader; Alu, Andrea
2006-03-01
In recent years metamaterials have offered new possibilities for overcoming some of the intrinsic limitations in wave propagation. Their realization at microwave frequencies has followed two different paths; one consisting of embedding resonant inclusions in a host dielectric, and the other following a transmission-line approach, i.e., building 1-D, 2-D, or 3-D cascades of circuit elements, respectively, as linear, planar or bulk right- or left-handed metamaterials. The latter is known to provide larger bandwidth and better robustness to ohmic losses. Extending these concepts to optical frequencies is a challenging task, due to changes in material response to electromagnetic waves at these frequencies. However, recently we have studied theoretically how it may be possible to have circuit nano-elements at these frequencies by properly exploiting plasmonic resonances. Here we present our theoretical work on translating the circuit concepts of right- and left-handed metamaterials into optical frequencies by applying the analogy between nanoparticles and nanocircuit elements in transmission lines. We discuss how it is possible to synthesize optical negative-refraction metamaterials by properly cascading plasmonic and non-plasmonic elements in 1-D, 2-D and 3-D geometries.
Introduction to string and superstring theory II
Peskin, M.E.
1987-03-01
Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic and the computation of scattering amplitudes are discussed. The formalism used is extended to clarify the origin of Yang-Mills gauge invariance in the open bosonic string theory. The question of the general-coordinate gauge invariance of string theory is addressed, presenting two disparate viewpoints on this question. A brief introduction is then given of the reduction from the idealized string theory in 10 extended dimensions to more realistic solutions in which all but 4 of these dimensions are compactified. The state of knowledge about the space-time supersymmetry of the superstring from the covariant viewpoint is outlined. An approach for identifying possible 6-dimensional spaces which might represent the form of the compact dimensions is discussed, and the orbifold scheme of compactification is presented. 77 refs., 18 figs. (LEW)
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
2009-03-01
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
NASA Astrophysics Data System (ADS)
Dittrich, B.; Thiemann, T.
2006-02-01
This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein Yang Mills theory and 2 + 1 gravity. Interestingly, while Yang Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity.
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
NASA Astrophysics Data System (ADS)
Frost, James E.; Jones, Garth A.
2014-11-01
The objective of this study is to investigate under what circumstances Förster theory of electronic (resonance) energy transfer breaks down in molecular aggregates. This is achieved by simulating the dynamics of exciton diffusion, on the femtosecond timescale, in molecular aggregates using the Liouville-von Neumann equation of motion. Specifically the focus of this work is the investigation of both spatial and temporal deviations between exciton dynamics driven by electronic couplings calculated from Förster theory and those calculated from quantum electrodynamics. The quantum electrodynamics (QED) derived couplings contain medium- and far-zone terms that do not exist in Förster theory. The results of the simulations indicate that Förster coupling is valid when the dipole centres are within a few nanometres of one another. However, as the distance between the dipole centres increases from 2 nm to 10 nm, the intermediate- and far-zone coupling terms play non-negligible roles and Förster theory begins to break down. Interestingly, the simulations illustrate how contributions to the exciton dynamics from the intermediate- and far-zone coupling terms of QED are quickly washed-out by the near-zone mechanism of Förster theory for lattices comprising closely packed molecules. On the other hand, in the case of sparsely packed arrays, the exciton dynamics resulting from the different theories diverge within the 100 fs lifetime of the trajectories. These results could have implications for the application of spectroscopic ruler techniques as well as design principles relating to energy harvesting materials.
NASA Astrophysics Data System (ADS)
Cheng, Chingyun; Kangara, Jayampathi; Arakelyan, Ilya; Thomas, John
2016-05-01
We tune the dimensionality of a strongly interacting degenerate 6 Li Fermi gas from 2D to quasi-2D, by adjusting the radial confinement of pancake-shaped clouds to control the radial chemical potential. In the 2D regime with weak radial confinement, the measured pair binding energies are in agreement with 2D-BCS mean field theory, which predicts dimer pairing energies in the many-body regime. In the qausi-2D regime obtained with increased radial confinement, the measured pairing energy deviates significantly from 2D-BCS theory. In contrast to the pairing energy, the measured radii of the cloud profiles are not fit by 2D-BCS theory in either the 2D or quasi-2D regimes, but are fit in both regimes by a beyond mean field polaron-model of the free energy. Supported by DOE, ARO, NSF, and AFOSR.
ERIC Educational Resources Information Center
Rias, Riaza Mohd; Zaman, Halimah Badioze
2011-01-01
Higher learning based instruction may be primarily concerned in most cases with the content of their academic lessons, and not very much with their instructional delivery. However, the effective application of learning theories and technology in higher education has an impact on student performance. With the rapid progress in the computer and…
Supersymmetry and String Theory
NASA Astrophysics Data System (ADS)
Dine, Michael
2016-01-01
Preface to the first edition; Preface to the second edition; A note on choice of metric; Text website; Part I. Effective Field Theory: The Standard Model, Supersymmetry, Unification: 1. Before the Standard Model; 2. The Standard Model; 3. Phenomenology of the Standard Model; 4. The Standard Model as an effective field theory; 5. Anomalies, instantons and the strong CP problem; 6. Grand unification; 7. Magnetic monopoles and solitons; 8. Technicolor: a first attempt to explain hierarchies; Part II. Supersymmetry: 9. Supersymmetry; 10. A first look at supersymmetry breaking; 11. The Minimal Supersymmetric Standard Model; 12. Supersymmetric grand unification; 13. Supersymmetric dynamics; 14. Dynamical supersymmetry breaking; 15. Theories with more than four conserved supercharges; 16. More supersymmetric dynamics; 17. An introduction to general relativity; 18. Cosmology; 19. Astroparticle physics and inflation; Part III. String Theory: 20. Introduction; 21. The bosonic string; 22. The superstring; 23. The heterotic string; 24. Effective actions in ten dimensions; 25. Compactification of string theory I. Tori and orbifolds; 26. Compactification of string theory II. Calabi-Yau compactifications; 27. Dynamics of string theory at weak coupling; 28. Beyond weak coupling: non-perturbative string theory; 29. Large and warped extra dimensions; 30. The landscape: a challenge to the naturalness principle; 31. Coda: where are we headed?; Part IV. The Appendices: Appendix A. Two-component spinors; Appendix B. Goldstone's theorem and the pi mesons; Appendix C. Some practice with the path integral in field theory; Appendix D. The beta function in supersymmetric Yang-Mills theory; References; Index.
2D semiconductor optoelectronics
NASA Astrophysics Data System (ADS)
Novoselov, Kostya
The advent of graphene and related 2D materials has recently led to a new technology: heterostructures based on these atomically thin crystals. The paradigm proved itself extremely versatile and led to rapid demonstration of tunnelling diodes with negative differential resistance, tunnelling transistors, photovoltaic devices, etc. By taking the complexity and functionality of such van der Waals heterostructures to the next level we introduce quantum wells engineered with one atomic plane precision. Light emission from such quantum wells, quantum dots and polaritonic effects will be discussed.
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.
NASA Astrophysics Data System (ADS)
Komninos, Yannis; Nicolaides, Cleanthes A.
2004-05-01
In continuation of our earlier work on the ab initio calculation of perturbed spectra and on a corresponding quantum defect theory (QDT), we discuss certain essential characteristics having to do with the unification of the continuous and the discrete spectra via the formal and practical construction of smooth quantities without invoking the pair of analytic forms of regular and irregular functions. The theory and its computational methodology are in the framework of configuration interaction (CI), and its structure shows how wavefunctions and properties of excited states of atoms and molecules can be computed provided one uses reliable zero-order basis functions, regardless of whether the relevant potential is, asymptotically, Coulombic or some other type. The mathematical connection with smooth reaction matrices in the discrete spectrum is demonstrated via the Mittag-Leffler theorem for the construction of analytic functions. We compare results for the quantum defects and fine structure from the present theory, as implemented by Komninos et al ( 1995 J. Phys. B: At. Mol. Opt. Phys. 28 2049 , 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L193 ), of the Al spectra of 2 D symmetry (strongly perturbed) and of 2 F o symmetry (weakly perturbed), with the recently reported measurements on high-lying states ( Dyubko et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 3797 and 4827 ), as well as with those of Eriksson and Isberg (1963 Ark. Fys. 23 527) for the low-lying states. The comparison reveals for the first time very good agreement between theory and experiment for both series. In addition, predictions for the other states of the series are made. Previous computations of the quantum defects of the 2 D spectrum, in general, do not agree among themselves while they deviate from the experimental values.
Ultraviolet divergences in non-renormalizable supersymmetric theories
NASA Astrophysics Data System (ADS)
Smilga, A.
2017-03-01
We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4 D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.
Schwarzschild Black Holes from Matrix Theory
Banks, T.; Fischler, W.; Klebanov, I.R.; Susskind, L.
1998-01-01
We consider matrix theory compactified on T{sup 3} and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional supersymmetric Yang-Mills theory with 16supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski. {copyright} {ital 1998} {ital The American Physical Society}
Gauge Theories on the Coulomb Branch
NASA Astrophysics Data System (ADS)
Schwarz, John H.
We construct the world-volume action of a probe D3-brane in AdS5 × S5 with N units of flux. It has the field content, symmetries, and dualities of the U(1) factor of 𝒩 = 4 U(N + 1) super Yang-Mills theory, spontaneously broken to U(N) × U(1) by being on the Coulomb branch, with the massive fields integrated out. This motivates the conjecture that it is the exact effective action, called a highly effective action (HEA). We construct an SL(2, Z) multiplet of BPS soliton solutions of the D3-brane theory (the conjectured HEA) and show that they reproduce the electrically charged massive states that have been integrated out as well as magnetic monopoles and dyons. Their charges are uniformly spread on a spherical surface, called a soliton bubble, which is interpreted as a phase boundary.
NASA Astrophysics Data System (ADS)
Isegawa, Miho; Liu, Fengyi; Maeda, Satoshi; Morokuma, Keiji
2014-10-01
We report reaction paths starting from N(2D) + H2O for doublet spin states, D0 and D1. The potential energy surfaces are explored in an automated fashion using the global reaction route mapping strategy. The critical points and reaction paths have been fully optimized at the complete active space second order perturbation theory level taking all valence electrons in the active space. In addition to direct dissociation pathways that would be dominant, three roaming processes, two roaming dissociation, and one roaming isomerization: (1) H2ON → H-O(H)N → H-HON → NO(2Π) + H2, (2) cis-HNOH → HNO-H → H-HNO → NO + H2, (3) H2NO → H-HNO → HNO-H → trans-HNOH, are confirmed on the D0 surface.
Ouk, Chanda-Malis; Zvereva-Loëte, Natalia; Scribano, Yohann; Bussery-Honvault, Béatrice
2012-10-30
Multireference single and double configuration interaction (MRCI) calculations including Davidson (+Q) or Pople (+P) corrections have been conducted in this work for the reactants, products, and extrema of the doublet ground state potential energy surface involved in the N((2)D) + CH(4) reaction. Such highly correlated ab initio calculations are then compared with previous PMP4, CCSD(T), W1, and DFT/B3LYP studies. Large relative differences are observed in particular for the transition state in the entrance channel resolving the disagreement between previous ab initio calculations. We confirm the existence of a small but positive potential barrier (3.86 ± 0.84 kJ mol(-1) (MR-AQCC) and 3.89 kJ mol(-1) (MRCI+P)) in the entrance channel of the title reaction. The correlation is seen to change significantly the energetic position of the two minima and five saddle points of this system together with the dissociation channels but not their relative order. The influence of the electronic correlation into the energetic of the system is clearly demonstrated by the thermal rate constant evaluation and it temperature dependance by means of the transition state theory. Indeed, only MRCI values are able to reproduce the experimental rate constant of the title reaction and its behavior with temperature. Similarly, product branching ratios, evaluated by means of unimolecular RRKM theory, confirm the NH production of Umemoto et al., whereas previous works based on less accurate ab initio calculations failed. We confirm the previous findings that the N((2)D) + CH(4) reaction proceeds via an insertion-dissociation mechanism and that the dominant product channels are CH(2)NH + H and CH(3) + NH.
Sasakian quiver gauge theory on the Aloff-Wallach space X1,1
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.
2017-03-01
We consider the SU (3)-equivariant dimensional reduction of gauge theories on spaces of the form Md ×X1,1 with d-dimensional Riemannian manifold Md and the Aloff-Wallach space X1,1 = SU (3) / U (1) endowed with its Sasaki-Einstein structure. The condition of SU (3)-equivariance of vector bundles, which has already occurred in the studies of Spin (7)-instantons on cones over Aloff-Wallach spaces, is interpreted in terms of quiver diagrams, and we construct the corresponding quiver bundles, using (parts of) the weight diagram of SU (3). We consider three examples thereof explicitly and then compare the results with the quiver gauge theory on Q3 = SU (3) / (U (1) × U (1)), the leaf space underlying the Sasaki-Einstein manifold X1,1. Moreover, we study instanton solutions on the metric cone C (X1,1) by evaluating the Hermitian Yang-Mills equation. We briefly discuss some features of the moduli space thereof, following the main ideas of a treatment of Hermitian Yang-Mills instantons on cones over generic Sasaki-Einstein manifolds in the literature.
Seiberg-Witten theory as a Fermi gas
NASA Astrophysics Data System (ADS)
Bonelli, Giulio; Grassi, Alba; Tanzini, Alessandro
2017-01-01
We explore a new connection between Seiberg-Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang-Mills theory in a self-dual Ω background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlevé III_3 τ function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local P^1 × P^1 geometry.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories.
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F
2017-03-10
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS_{6}×S^{2} warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p,q) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Entanglement temperature for the excitation of SYM theory in the (de)confinement phase
NASA Astrophysics Data System (ADS)
Ghoroku, Kazuo; Ishihara, Masafumi
2015-10-01
We study the holographic supersymmetric Yang-Mills (SYM) theory, which is living in a hyperbolic space, in terms of the entanglement entropy. The theory contains a parameter C corresponding to the excitation of the SYM theory, and it controls the dynamical properties of the theory. The entanglement temperature, Tent , is obtained by imposing the thermodynamic law for the relative entanglement entropy and the energy density of the excitation. This temperature is available at any value of the parameter C even in the region where the Hawking temperature disappears. With this new temperature, the dynamical properties of the excited SYM theory are examined in terms of the thermodynamic law. We could find the signatures of phase transitions of the theory.
Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory.
Tourkine, Piotr; Vanhove, Pierre
2016-11-18
The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalization of the monodromy construction was lacking. In this Letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and nonplanar topologies in string theory. We write one and two-loop monodromy formulas explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulas by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.
E-2D Advanced Hawkeye Aircraft (E-2D AHE)
2015-12-01
Selected Acquisition Report (SAR) RCS: DD-A&T(Q&A)823-364 E-2D Advanced Hawkeye Aircraft (E-2D AHE) As of FY 2017 President’s Budget Defense...Office Estimate RDT&E - Research, Development, Test, and Evaluation SAR - Selected Acquisition Report SCP - Service Cost Position TBD - To Be Determined
Synchrotron radiation in strongly coupled conformal field theories
Athanasiou, Christiana; Chesler, Paul M.; Liu, Hong; Rajagopal, Krishna; Nickel, Dominik
2010-06-15
Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled N=4 supersymmetric Yang-Mills theory. We compare the strong coupling results to those at weak coupling, finding them to be very similar. In both regimes, the angular distribution of the radiated power is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle {alpha}{approx}1/{gamma}. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.
On S-Duality in Abelian Gauge Theory
NASA Astrophysics Data System (ADS)
Witten, Edward
1995-09-01
U(1) gauge theory on R4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises when N=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b+2≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.
Gauge formulation of gravitation theories. I. The Poincaré, de Sitter, and conformal cases
NASA Astrophysics Data System (ADS)
Ivanov, E. A.; Niederle, J.
1982-02-01
The gauge formulations of various gravitation theories are discussed. They are based on the approach in which we have the group Diff R4 acting on xμ and in which we attach to every xμ a tangent space with the group of action H. Group H does not act on xμ and plays the role of an internal (global) symmetry group in the standard Yang-Mills theory. The matter fields in the theory transform according to representations of H and are assumed to be scalars of Diff R4. The full invariance group of the Lagrangian is then of the form Hloc⊗Diff R4. Here Hloc is a local gauge group obtained from H exactly as in the Yang-Mills theory. The approach has two characteristic features: (i) The group Hloc must be spontaneously broken in order to exclude redundant gauge fields (the Lorentz connections) from the theory in a way covariant with respect to the gauge transformations. (ii) To different H there correspond different gravitational theories, all invariant under Diff R4 but differing in backgrounds. Thus if H is isomorphic to the Poincaré group the corresponding gauge theory turns out to be equivalent to the usual Einstein or Einstein-Cartan theory of gravity in the Minkowski space as a background. The other choices for H considered in the paper are the de Sitter groups and the conformal group. They yield the Einstein theory with a negative (or positive) cosmological term in the corresponding de Sitter space and the Weyl or Cartan-Weyl theory (depending on realization of the conformal group), respectively.
Isegawa, Miho; Liu, Fengyi; Maeda, Satoshi; Morokuma, Keiji
2014-10-21
We report reaction paths starting from N({sup 2}D) + H{sub 2}O for doublet spin states, D{sub 0} and D{sub 1}. The potential energy surfaces are explored in an automated fashion using the global reaction route mapping strategy. The critical points and reaction paths have been fully optimized at the complete active space second order perturbation theory level taking all valence electrons in the active space. In addition to direct dissociation pathways that would be dominant, three roaming processes, two roaming dissociation, and one roaming isomerization: (1) H{sub 2}ON → H–O(H)N → H–HON → NO({sup 2}Π) + H{sub 2}, (2) cis-HNOH → HNO–H → H–HNO → NO + H{sub 2}, (3) H{sub 2}NO → H–HNO → HNO–H → trans-HNOH, are confirmed on the D{sub 0} surface.
Higher spin approaches to quantum field theory and (psuedo)-Riemannian geometries
NASA Astrophysics Data System (ADS)
Hallowell, Karl Evan
In this thesis, we study a number of higher spin quantum field theories and some of their algebraic and geometric consequences. These theories apply mostly either over constant curvature or more generally symmetric pseudo-Riemannian manifolds. The first part of this dissertation covers a superalgebra coming from a family of particle models over symmetric spaces. These theories are novel in that the symmetries of the (super)algebra osp( Q|2p) are larger and more elaborate than traditional symmetries. We construct useful (super)algebras related to and generalizing old work by Lichnerowicz and describe their role in developing the geometry of massless models with osp(Q|2 p) symmetry. The result is two practical applications of these (super)algebras: (1) a lunch more concise description of a family of higher spin quantum field theories; and (2) an interesting algebraic probe of underlying background geometries. We also consider massive models over constant curvature spaces. We use a radial dimensional reduction process which converts massless models into massive ones over a lower dimensional space. In our case, we take from the family of theories above the particular free, massless model over flat space associated with sp(2, R ) and derive a massive model. In the process, we develop a novel associative algebra, which is a deformation of the original differential operator algebra associated with the sp(2, R ) model. This algebra is interesting in its own right since its operators realize the representation structure of the sp(2, R ) group. The massive model also has implications for a sequence of unusual, "partially massless" theories. The derivation illuminates how reduced degrees of freedom become manifest in these particular models. Finally, we study a Yang-Mills model using an on-shell Poincare Yang-Mills twist of the Maxwell complex along with a non-minimal coupling. This is a special, higher spin case of a quantum field theory called a Yang-Mills detour complex
Connection dynamics of higher-dimensional scalar-tensor theories of gravity
NASA Astrophysics Data System (ADS)
Han, Yu; Ma, Yongge; Zhang, Xiangdong
2014-09-01
The scalar-tensor theories (STTs) of gravity in spacetime dimensions (D+1)>2 are studied. By performing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structures in both sectors are similar to the corresponding structures of four-dimensional cases. It turns out that, similar to the case of general relativity (GR), there is also a symplectic reduction from the canonical structure of so(D+1) Yang-Mills theories coupled to the scalar field to the canonical structure of the geometrical STTs. Therefore, the non-perturbative loop quantum (LQG) gravity techniques can also be applied to the STTs in D+1 dimensions based on their connection-dynamical formalism.
Lectures on the plane-wave string/gauge theory duality
NASA Astrophysics Data System (ADS)
Plefka, J. C.
2004-02-01
These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to = 4, d = 4, U(N) super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS5 × S5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter - in agreement with the string genus expansion for non-zero gs. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light-cone superstring field theory in a plane-wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane-wave string/gauge theory duality.
Integrating Mobile Multimedia into Textbooks: 2D Barcodes
ERIC Educational Resources Information Center
Uluyol, Celebi; Agca, R. Kagan
2012-01-01
The major goal of this study was to empirically compare text-plus-mobile phone learning using an integrated 2D barcode tag in a printed text with three other conditions described in multimedia learning theory. The method examined in the study involved modifications of the instructional material such that: a 2D barcode was used near the text, the…
Quantum walks and non-Abelian discrete gauge theory
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Di Molfetta, Giuseppe; Brachet, Marc; Debbasch, Fabrice
2016-07-01
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N ) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N ) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N ) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1 ) Maxwell fields and SU(N ) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2 ) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-07-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Optoelectronics with 2D semiconductors
NASA Astrophysics Data System (ADS)
Mueller, Thomas
2015-03-01
Two-dimensional (2D) atomic crystals, such as graphene and layered transition-metal dichalcogenides, are currently receiving a lot of attention for applications in electronics and optoelectronics. In this talk, I will review our research activities on electrically driven light emission, photovoltaic energy conversion and photodetection in 2D semiconductors. In particular, WSe2 monolayer p-n junctions formed by electrostatic doping using a pair of split gate electrodes, type-II heterojunctions based on MoS2/WSe2 and MoS2/phosphorene van der Waals stacks, 2D multi-junction solar cells, and 3D/2D semiconductor interfaces will be presented. Upon optical illumination, conversion of light into electrical energy occurs in these devices. If an electrical current is driven, efficient electroluminescence is obtained. I will present measurements of the electrical characteristics, the optical properties, and the gate voltage dependence of the device response. In the second part of my talk, I will discuss photoconductivity studies of MoS2 field-effect transistors. We identify photovoltaic and photoconductive effects, which both show strong photoconductive gain. A model will be presented that reproduces our experimental findings, such as the dependence on optical power and gate voltage. We envision that the efficient photon conversion and light emission, combined with the advantages of 2D semiconductors, such as flexibility, high mechanical stability and low costs of production, could lead to new optoelectronic technologies.
The Theory of High Energy Collision Processes - Final Report DOE/ER/40158-1
Wu, Tai, T.
2011-09-15
In 1984, DOE awarded Harvard University a new Grant DE-FG02-84ER40158 to continue their support of Tai Tsun Wu as Principal Investigator of research on the theory of high energy collision processes. This Grant was renewed and remained active continuously from June 1, 1984 through November 30, 2007. Topics of interest during the 23-year duration of this Grant include: the theory and phenomenology of collision and production processes at ever higher energies; helicity methods of QED and QCD; neutrino oscillations and masses; Yang-Mills gauge theory; Beamstrahlung; Fermi pseudopotentials; magnetic monopoles and dyons; cosmology; classical confinement; mass relations; Bose-Einstein condensation; and large-momentum-transfer scattering processes. This Final Report describes the research carried out on Grant DE-FG02-84ER40158 for the period June 1, 1984 through November 30, 2007. Two books resulted from this project and a total of 125 publications.
Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time
NASA Astrophysics Data System (ADS)
Benisty, David; Guendelman, E. I.
2016-09-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.
Computational Screening of 2D Materials for Photocatalysis.
Singh, Arunima K; Mathew, Kiran; Zhuang, Houlong L; Hennig, Richard G
2015-03-19
Two-dimensional (2D) materials exhibit a range of extraordinary electronic, optical, and mechanical properties different from their bulk counterparts with potential applications for 2D materials emerging in energy storage and conversion technologies. In this Perspective, we summarize the recent developments in the field of solar water splitting using 2D materials and review a computational screening approach to rapidly and efficiently discover more 2D materials that possess properties suitable for solar water splitting. Computational tools based on density-functional theory can predict the intrinsic properties of potential photocatalyst such as their electronic properties, optical absorbance, and solubility in aqueous solutions. Computational tools enable the exploration of possible routes to enhance the photocatalytic activity of 2D materials by use of mechanical strain, bias potential, doping, and pH. We discuss future research directions and needed method developments for the computational design and optimization of 2D materials for photocatalysis.
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Remarks on thermalization in 2D CFT
NASA Astrophysics Data System (ADS)
de Boer, Jan; Engelhardt, Dalit
2016-12-01
We revisit certain aspects of thermalization in 2D conformal field theory (CFT). In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a Banados-Teitelboim-Zanelli black hole. The extra conserved charges, while rendering c <1 theories essentially integrable, therefore seem to have little effect on large-c conformal field theories.
Highly crystalline 2D superconductors
NASA Astrophysics Data System (ADS)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2016-12-01
Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.
Sevrin, A.
1993-06-01
After reviewing some aspects of gravity in two dimensions, I show that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given.
Sum rules and spectral density flow in QCD and in superconformal theories
NASA Astrophysics Data System (ADS)
Costantini, Antonio; Delle Rose, Luigi; Serino, Mirko
2014-11-01
We discuss the signature of the anomalous breaking of the superconformal symmetry in N = 1 super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the N = 1 theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD) multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.
Phylogenetic tree construction based on 2D graphical representation
NASA Astrophysics Data System (ADS)
Liao, Bo; Shan, Xinzhou; Zhu, Wen; Li, Renfa
2006-04-01
A new approach based on the two-dimensional (2D) graphical representation of the whole genome sequence [Bo Liao, Chem. Phys. Lett., 401(2005) 196.] is proposed to analyze the phylogenetic relationships of genomes. The evolutionary distances are obtained through measuring the differences among the 2D curves. The fuzzy theory is used to construct phylogenetic tree. The phylogenetic relationships of H5N1 avian influenza virus illustrate the utility of our approach.
BOOK REVIEW: Supersymmetry and String Theory: Beyond the Standard Model
NASA Astrophysics Data System (ADS)
Rocek, Martin
2007-11-01
When I was asked to review Michael Dine's new book, 'Supersymmetry and String Theory', I was pleased to have a chance to read a book by such an established authority on how string theory might become testable. The book is most useful as a list of current topics of interest in modern theoretical physics. It gives a succinct summary of a huge variety of subjects, including the standard model, symmetry, Yang Mills theory, quantization of gauge theories, the phenomenology of the standard model, the renormalization group, lattice gauge theory, effective field theories, anomalies, instantons, solitons, monopoles, dualities, technicolor, supersymmetry, the minimal supersymmetric standard model, dynamical supersymmetry breaking, extended supersymmetry, Seiberg Witten theory, general relativity, cosmology, inflation, bosonic string theory, the superstring, the heterotic string, string compactifications, the quintic, string dualities, large extra dimensions, and, in the appendices, Goldstone's theorem, path integrals, and exact beta-functions in supersymmetric gauge theories. Its breadth is both its strength and its weakness: it is not (and could not possibly be) either a definitive reference for experts, where the details of thorny technical issues are carefully explored, or a textbook for graduate students, with detailed pedagogical expositions. As such, it complements rather than replaces the much narrower and more focussed String Theory I and II volumes by Polchinski, with their deep insights, as well the two older volumes by Green, Schwarz, and Witten, which develop string theory pedagogically.
Supergravity Duals of Matrix String Theory
NASA Astrophysics Data System (ADS)
Morales, Jose F.; Samtleben, Henning
2002-08-01
We study holographic duals of type II and heterotic matrix string theories described by warped AdS3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS3 × S7. The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the Script N = (8,8), Script N = (8,0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,bar h) = (3/2,3/2) twisted operator which brings the matrix string theories out from the conformal point (Bbb R8)N/SN with the dilaton profile in the supergravity background. The familiar dictionary between masses and ``scaling'' dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdSd+1 × Sq geometries and super Yang-Mills theories with 16 supercharges.
Test of the Anti-de Sitter-Space/Conformal-Field-Theory Correspondence Using High-Spin Operators
Benna, M. K.; Benvenuti, S.; Klebanov, I. R.; Scardicchio, A.
2007-03-30
In two remarkable recent papers the planar perturbative expansion was proposed for the universal function of the coupling appearing in the dimensions of high-spin operators of the N=4 super Yang-Mills theory. We study numerically the integral equation derived by Beisert, Eden, and Staudacher, which resums the perturbative series. In a confirmation of the anti-de Sitter-space/conformal-field-theory (AdS/CFT) correspondence, we find a smooth function whose two leading terms at strong coupling match the results obtained for the semiclassical folded string spinning in AdS{sub 5}. We also make a numerical prediction for the third term in the strong coupling series.
Anisotropic heavy quark potential in strongly-coupled N =4 SYM theory in a magnetic field
NASA Astrophysics Data System (ADS)
Rougemont, R.; Critelli, R.; Noronha, J.
2015-03-01
In this work we use the gauge/gravity duality to study the anisotropy in the heavy quark potential in strongly coupled N =4 super-Yang Mills (SYM) theory (both at zero and nonzero temperature) induced by a constant and uniform magnetic field B . At zero temperature, the inclusion of the magnetic field decreases the attractive force between heavy quarks with respect to its B =0 value and the force associated with the parallel potential is the least attractive force. We find that the same occurs at nonzero temperature and, thus, at least in the case of strongly coupled N =4 SYM, the presence of a magnetic field generally weakens the interaction between heavy quarks in the plasma.
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.
The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions
NASA Astrophysics Data System (ADS)
Mazilu, Nicolae; Agop, Maricel; Gatu, Irina; Iacob, Dan Dezideriu; Butuc, Irina; Ghizdovat, Vlad
2016-06-01
The color is an interaction property: of the interaction of light with matter. Classically speaking it is therefore akin to the forces. But while forces engendered the mechanical view of the world, the colors generated the optical view. One of the modern concepts of interaction between the fundamental particles of matter - the quantum chromodynamics - aims to fill the gap between mechanics and optics, in a specific description of strong interactions. We show here that this modern description of the particle interactions has ties with both the classical and quantum theories of light, regardless of the connection between forces and colors. In a word, the light is a universal model in the description of matter. The description involves classical Yang-Mills fields related to color.
2D quasiperiodic plasmonic crystals
Bauer, Christina; Kobiela, Georg; Giessen, Harald
2012-01-01
Nanophotonic structures with irregular symmetry, such as quasiperiodic plasmonic crystals, have gained an increasing amount of attention, in particular as potential candidates to enhance the absorption of solar cells in an angular insensitive fashion. To examine the photonic bandstructure of such systems that determines their optical properties, it is necessary to measure and model normal and oblique light interaction with plasmonic crystals. We determine the different propagation vectors and consider the interaction of all possible waveguide modes and particle plasmons in a 2D metallic photonic quasicrystal, in conjunction with the dispersion relations of a slab waveguide. Using a Fano model, we calculate the optical properties for normal and inclined light incidence. Comparing measurements of a quasiperiodic lattice to the modelled spectra for angle of incidence variation in both azimuthal and polar direction of the sample gives excellent agreement and confirms the predictive power of our model. PMID:23209871
NASA Astrophysics Data System (ADS)
Schaibley, John R.; Yu, Hongyi; Clark, Genevieve; Rivera, Pasqual; Ross, Jason S.; Seyler, Kyle L.; Yao, Wang; Xu, Xiaodong
2016-11-01
Semiconductor technology is currently based on the manipulation of electronic charge; however, electrons have additional degrees of freedom, such as spin and valley, that can be used to encode and process information. Over the past several decades, there has been significant progress in manipulating electron spin for semiconductor spintronic devices, motivated by potential spin-based information processing and storage applications. However, experimental progress towards manipulating the valley degree of freedom for potential valleytronic devices has been limited until very recently. We review the latest advances in valleytronics, which have largely been enabled by the isolation of 2D materials (such as graphene and semiconducting transition metal dichalcogenides) that host an easily accessible electronic valley degree of freedom, allowing for dynamic control.
Microwave Assisted 2D Materials Exfoliation
NASA Astrophysics Data System (ADS)
Wang, Yanbin
Two-dimensional materials have emerged as extremely important materials with applications ranging from energy and environmental science to electronics and biology. Here we report our discovery of a universal, ultrafast, green, solvo-thermal technology for producing excellent-quality, few-layered nanosheets in liquid phase from well-known 2D materials such as such hexagonal boron nitride (h-BN), graphite, and MoS2. We start by mixing the uniform bulk-layered material with a common organic solvent that matches its surface energy to reduce the van der Waals attractive interactions between the layers; next, the solutions are heated in a commercial microwave oven to overcome the energy barrier between bulk and few-layers states. We discovered the minutes-long rapid exfoliation process is highly temperature dependent, which requires precise thermal management to obtain high-quality inks. We hypothesize a possible mechanism of this proposed solvo-thermal process; our theory confirms the basis of this novel technique for exfoliation of high-quality, layered 2D materials by using an as yet unknown role of the solvent.
Quantum coherence selective 2D Raman–2D electronic spectroscopy
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-01-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational–vibrational, electronic–vibrational and electronic–electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment–protein complexes. PMID:28281541
Quantum coherence selective 2D Raman-2D electronic spectroscopy
NASA Astrophysics Data System (ADS)
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-03-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
Quantum coherence selective 2D Raman-2D electronic spectroscopy.
Spencer, Austin P; Hutson, William O; Harel, Elad
2017-03-10
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
Supersymmetric M5 brane theories on R × CP2
NASA Astrophysics Data System (ADS)
Kim, Hee-Cheol; Lee, Kimyeong
2013-07-01
We propose 4 and 12 supersymmetric conformal Yang-Mills-Chern-Simons theories on R × CP2 as multiple representations of the theory on M5 branes. These theories are obtained by twisted Zk modding and dimensional reduction of the 6d (2,0) superconformal field theory on R × S5 and have a discrete coupling constant 1/{g_{{YM}^2}}=k/{4{π^2}} with natural number k. Instantons in these theories are expected to represent the Kaluza-Klein modes. For the k = 1 , 2 cases, we argue that the number of supersymmetries in our theories should be enhanced to 32 and 16, respectively. For the k = 3 case, only the 4 supersymmetric theory gets the supersymmetric enhancement to 8. For the 4 supersymmetric case, the vacuum structure becomes more complicated as there are degenerate supersymmetric vacua characterized by fuzzy spheres. We calculate the perturbative part of the SU( N ) gauge group Euclidean path integral for the index function at the symmetric phase of the 4 supersymmetric case and confirm it with the known half-BPS index. From the similar twisted Z k modding of the AdS7 × S4 geometry, we speculate that the M region is for k ≲ N 1/3 and the type IIA region is N 1/3 ≲ k ≲ N. When nonperturbative corrections are included, our theories are expected to produce the full index of the 6d (2,0) theory.
2D quantum gravity from quantum entanglement.
Gliozzi, F
2011-01-21
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.
Canard configured aircraft with 2-D nozzle
NASA Technical Reports Server (NTRS)
Child, R. D.; Henderson, W. P.
1978-01-01
A closely-coupled canard fighter with vectorable two-dimensional nozzle was designed for enhanced transonic maneuvering. The HiMAT maneuver goal of a sustained 8g turn at a free-stream Mach number of 0.9 and 30,000 feet was the primary design consideration. The aerodynamic design process was initiated with a linear theory optimization minimizing the zero percent suction drag including jet effects and refined with three-dimensional nonlinear potential flow techniques. Allowances were made for mutual interference and viscous effects. The design process to arrive at the resultant configuration is described, and the design of a powered 2-D nozzle model to be tested in the LRC 16-foot Propulsion Wind Tunnel is shown.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
NKG2D ligands as therapeutic targets
Spear, Paul; Wu, Ming-Ru; Sentman, Marie-Louise; Sentman, Charles L.
2013-01-01
The Natural Killer Group 2D (NKG2D) receptor plays an important role in protecting the host from infections and cancer. By recognizing ligands induced on infected or tumor cells, NKG2D modulates lymphocyte activation and promotes immunity to eliminate ligand-expressing cells. Because these ligands are not widely expressed on healthy adult tissue, NKG2D ligands may present a useful target for immunotherapeutic approaches in cancer. Novel therapies targeting NKG2D ligands for the treatment of cancer have shown preclinical success and are poised to enter into clinical trials. In this review, the NKG2D receptor and its ligands are discussed in the context of cancer, infection, and autoimmunity. In addition, therapies targeting NKG2D ligands in cancer are also reviewed. PMID:23833565
2D microscopic model of graphene fracture properties
NASA Astrophysics Data System (ADS)
Hess, Peter
2015-05-01
An analytical two-dimensional (2D) microscopic fracture model based on Morse-type interaction is derived containing no adjustable parameter. From the 2D Young’s moduli and 2D intrinsic strengths of graphene measured by nanoindentation based on biaxial tension and calculated by density functional theory for uniaxial tension the widely unknown breaking force, line or edge energy, surface energy, fracture toughness, and strain energy release rate were determined. The simulated line energy agrees well with ab initio calculations and the fracture toughness of perfect graphene sheets is in good agreement with molecular dynamics simulations and the fracture toughness evaluated for defective graphene using the Griffith relation. Similarly, the estimated critical strain energy release rate agrees well with result of various theoretical approaches based on the J-integral and surface energy. The 2D microscopic model, connecting 2D and three-dimensional mechanical properties in a consistent way, provides a versatile relationship to easily access all relevant fracture properties of pristine 2D solids.
Local subsystems in gauge theory and gravity
NASA Astrophysics Data System (ADS)
Donnelly, William; Freidel, Laurent
2016-09-01
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of localized subsystems. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.
Interpolating the Coulomb phase of little string theory
Lin, Ying -Hsuan; Shao, Shu -Heng; Wang, Yifan; ...
2015-12-03
We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity onmore » the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. As a result, we also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.« less
Interpolating the Coulomb phase of little string theory
Lin, Ying -Hsuan; Shao, Shu -Heng; Wang, Yifan; Yin, Xi
2015-12-03
We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. As a result, we also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.
Quantitative 2D liquid-state NMR.
Giraudeau, Patrick
2014-06-01
Two-dimensional (2D) liquid-state NMR has a very high potential to simultaneously determine the absolute concentration of small molecules in complex mixtures, thanks to its capacity to separate overlapping resonances. However, it suffers from two main drawbacks that probably explain its relatively late development. First, the 2D NMR signal is strongly molecule-dependent and site-dependent; second, the long duration of 2D NMR experiments prevents its general use for high-throughput quantitative applications and affects its quantitative performance. Fortunately, the last 10 years has witnessed an increasing number of contributions where quantitative approaches based on 2D NMR were developed and applied to solve real analytical issues. This review aims at presenting these recent efforts to reach a high trueness and precision in quantitative measurements by 2D NMR. After highlighting the interest of 2D NMR for quantitative analysis, the different strategies to determine the absolute concentrations from 2D NMR spectra are described and illustrated by recent applications. The last part of the manuscript concerns the recent development of fast quantitative 2D NMR approaches, aiming at reducing the experiment duration while preserving - or even increasing - the analytical performance. We hope that this comprehensive review will help readers to apprehend the current landscape of quantitative 2D NMR, as well as the perspectives that may arise from it.
Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence
NASA Astrophysics Data System (ADS)
Harmark, Troels; Orselli, Marta
2014-11-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N). We show that SMT describes super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS5 × S 5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.
NASA Astrophysics Data System (ADS)
Jejjala, Vishnumohan
2002-01-01
This Thesis explores aspects of superstring theory on orbifold spaces and applies some of the intuition gleaned from the study of the non-commutative geometry of space-time to understanding the fractional quantum Hall effect. The moduli space of vacua of marginal and relevant deformations of N = 4 super-Yang-Mills gauge theory in four dimensions is interpreted in terms of non-commutative geometry. A formalism for thinking about the algebraic geometry of the moduli space is developed. Within this framework, the representation theory of the algebras studied provides a natural exposition of D-brane fractionation. The non-commutative moduli space of deformations preserving N = 1 supersymmetry is examined in detail through various examples. In string theory, by the AdS/CFT correspondence, deformations of the N = 4 field theory are dual to the near-horizon geometries of D-branes on orbifolds of AdS5 x S 5. The physics of D-branes on the dual AdS backgrounds is explored. Quivers encapsulate the matter content of supersymmetric field theories on the worldvolumes of D-branes at orbifold singularities. New techniques for constructing quivers are presented here. When N is a normal subgroup of a finite group G, the quiver corresponding to fixed points of the orbifold M/G is computed from a G/N action on the quiver corresponding to M/G . These techniques prove useful for constructing non-Abelian quivers and for examining discrete torsion orbifolds. Quivers obtained through our constructions contain interesting low-energy phenomenology. The matter content on a brane at an isolated singularity of the Delta27 orbifold embeds the Standard Model. The symmetries of the quiver require exactly three generations of fields in the particle spectrum. Lepton masses are suppressed relative to quark masses because lepton Yukawa couplings do not appear in the superpotential. Lepton masses are generated through the Kahler potential and are related to the supersymmetry breaking scale. The model
Sparse radar imaging using 2D compressed sensing
NASA Astrophysics Data System (ADS)
Hou, Qingkai; Liu, Yang; Chen, Zengping; Su, Shaoying
2014-10-01
Radar imaging is an ill-posed linear inverse problem and compressed sensing (CS) has been proved to have tremendous potential in this field. This paper surveys the theory of radar imaging and a conclusion is drawn that the processing of ISAR imaging can be denoted mathematically as a problem of 2D sparse decomposition. Based on CS, we propose a novel measuring strategy for ISAR imaging radar and utilize random sub-sampling in both range and azimuth dimensions, which will reduce the amount of sampling data tremendously. In order to handle 2D reconstructing problem, the ordinary solution is converting the 2D problem into 1D by Kronecker product, which will increase the size of dictionary and computational cost sharply. In this paper, we introduce the 2D-SL0 algorithm into the reconstruction of imaging. It is proved that 2D-SL0 can achieve equivalent result as other 1D reconstructing methods, but the computational complexity and memory usage is reduced significantly. Moreover, we will state the results of simulating experiments and prove the effectiveness and feasibility of our method.
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
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.
Combinatorial quantization of the Hamiltonian Chern-Simons theory II
NASA Astrophysics Data System (ADS)
Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.
Gauge invariance and radiative corrections in an extra dimensional theory
NASA Astrophysics Data System (ADS)
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Multigluon scattering in open superstring theory
Stieberger, Stephan; Taylor, Tomasz R.
2006-12-15
We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit ({alpha}{sup '}{yields}0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4, 5, and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals--generalized Euler integrals--which for N{>=}6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their {alpha}{sup '} expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O({alpha}{sup '2}), originate from the well-known {alpha}{sup '2} TrF{sup 4} effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in {alpha}{sup '}. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC)
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
NASA Astrophysics Data System (ADS)
Dekker, T.; de Zwart, S. T.; Willemsen, O. H.; Hiddink, M. G. H.; IJzerman, W. L.
2006-02-01
A prerequisite for a wide market acceptance of 3D displays is the ability to switch between 3D and full resolution 2D. In this paper we present a robust and cost effective concept for an auto-stereoscopic switchable 2D/3D display. The display is based on an LCD panel, equipped with switchable LC-filled lenticular lenses. We will discuss 3D image quality, with the focus on display uniformity. We show that slanting the lenticulars in combination with a good lens design can minimize non-uniformities in our 20" 2D/3D monitors. Furthermore, we introduce fractional viewing systems as a very robust concept to further improve uniformity in the case slanting the lenticulars and optimizing the lens design are not sufficient. We will discuss measurements and numerical simulations of the key optical characteristics of this display. Finally, we discuss 2D image quality, the switching characteristics and the residual lens effect.
2-d Finite Element Code Postprocessor
Sanford, L. A.; Hallquist, J. O.
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Vian, F.
1999-05-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.
Mass gap in Yang's theory of gravity
NASA Astrophysics Data System (ADS)
Mielke, Eckehard W.
2015-06-01
The quantization of a curvature-squared model of gravity, in the affine form proposed by Yang, is reconsidered in the path integral formulation. Due to its inherent Weyl invariance, sharing this with internal Yang-Mills fields, it or some of its topological generalizations are still a possible route to quantum gravity. Instanton type solutions with double duality properties exhibit a "vacuum degeneracy", i.e. a bifurcation into distinct classical Einsteinian backgrounds. For linearized fields, this conclusively induces a mass gap in the graviton spectrum, a feature which is an open problem in the quantization of internal Yang-Mills fields.
String theory and the dark glueball problem
NASA Astrophysics Data System (ADS)
Halverson, James; Nelson, Brent D.; Ruehle, Fabian
2017-02-01
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and Δ Neff bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
Predicting non-square 2D dice probabilities
NASA Astrophysics Data System (ADS)
Pender, G. A. T.; Uhrin, M.
2014-07-01
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability. Indeed, it was considered by Newton in 1664 (Newton 1967 The Mathematical Papers of Issac Newton vol I (Cambridge: Cambridge University Press) pp 60-1). In this paper we make progress on the 2D problem (which can be realized in 3D by considering a long cuboid, or alternatively a rectangular cross-sectioned dreidel). For the two-dimensional case we suggest that the ratio of the probabilities of landing on each of the two sides is given by \\frac{\\sqrt{{{k}^{2}}+{{l}^{2}}}-k}{\\sqrt{{{k}^{2}}+{{l}^{2}}}-l}\\frac{arctan \\frac{l}{k}}{arctan \\frac{k}{l}} where k and l are the lengths of the two sides. We test this theory both experimentally and computationally, and find good agreement between our theory, experimental and computational results. Our theory is known, from its derivation, to be an approximation for particularly bouncy or ‘grippy’ surfaces where the die rolls through many revolutions before settling. On real surfaces we would expect (and we observe) that the true probability ratio for a 2D die is a somewhat closer to unity than predicted by our theory. This problem may also have wider relevance in the testing of physics engines.
String Theory, Strongly Correlated Systems, and Duality Twists
NASA Astrophysics Data System (ADS)
Torres Chicon, Nesty Ray
In the first part of this dissertation (Chapter 1), I present a construction of a six dimensional (2,0)-theory model that describes the dynamics of the Fractional Quantum Hall Effect (FQHE). The FQHE appears as part of the low energy description of the Coulomb branch of the A1 (2,0)-theory formulated on a geometry (S 1 x R2)/Zk. At low-energy, the configuration is described in terms of a 4+1D supersymmetric Yang-Mills (SYM) theory on a cone (R2/Z k) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged "quasi-particles" are BPS strings of the (2,0)-theory wrapped on short cycles. In this framework, a W-boson can be modeled as a bound state of k quasi-particles, which can be used to understand the dynamics of the FQHE. In the second part of this dissertation (Chapters 2-3), I investigate the N=4 SYM theory compactified on a circle, with a varying coupling constant (Janus configuration) and an S-duality twist. I relate this setup to a three dimensional topological theory and to a dual string theory. The equality of these descriptions is exhibited by matching the operator algebra, and the dimensions of the Hilbert space. Additionally, this dissertation addresses a classic result in number theory, called quadratic reciprocity, using string theory language. I present a proof that quadratic reciprocity is a direct consequence of T-duality of Type-II string theory. This is demonstrated by analyzing a partition function of abelian N=4 SYM theory on a certain supersymmetry-preserving four-manifold with variable coupling constant and a SL(2,Z)-duality twist.
Knot invariants and M-theory: Hitchin equations, Chern-Simons actions, and surface operators
NASA Astrophysics Data System (ADS)
Dasgupta, Keshav; Errasti Díez, Verónica; Ramadevi, P.; Tatar, Radu
2017-01-01
Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N =4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well-defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-Abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show that both the localization equations and surface operators appear naturally from the Hamiltonian formalism of the theories. Knots and link invariants are then constructed using M2-brane states in both the models.
Summation of all-loop UV divergences in maximally supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Borlakov, A. T.; Kazakov, D. I.; Tolkachev, D. M.; Vlasenko, D. E.
2016-12-01
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.
On topological field theory representation of higher analogs of classical special functions
NASA Astrophysics Data System (ADS)
Gerasimov, Anton A.; Lebedev, Dimitri R.
2011-09-01
Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. Precisely the special functions such as Whittaker functions and Γ-function were identified with correlation functions in topological field theories on a two-dimensional disk. Mirror symmetry of the underlying topological field theory leads to a dual finite-dimensional integral representations reproducing classical integral representations for the corresponding special functions. The mirror symmetry interchanging infinite- and finite-dimensional integral representations provides an incarnation of the local Archimedean Langlands duality on the level of classical special functions. In this note we provide some directions to higher-dimensional generalizations of our previous results. In the first part we consider topological field theory representations of multiple local L-factors introduced by Kurokawa and expressed through multiple Barnes's Γ-functions. In the second part we are dealing with generalizations based on consideration of topological Yang-Mills theories on non-compact four-dimensional manifolds. Presumably, in analogy with the mirror duality in two-dimensions, S-dual description should be instrumental for deriving integral representations for a particular class of quantum field theory correlation functions and thus providing a new interesting class of special functions supplied with canonical integral representations.
D2-D1 phase transition of columnar liquid crystals
NASA Astrophysics Data System (ADS)
Sun, Y. F.; Swift, J.
1986-04-01
The D2-D1 phase transition in columnar liquid crystals of the HAT series [e.g., HAT11 (triphenelene hexa-n-dodecanoate)] is discussed within the framework of Landau theory. The order parameters which describe the transition are abstracted from a tensor density function, and are associated with two irreducible representations of the symmetry group of the high-temperature D2 phase. A mechanism for a first-order transition is then suggested in accordance with both theoretical considerations and the experimental result for the D2-D1 transition. Two possible arrangements of the herringbone structure of the D1 phase are obtained, each of which gives six orientational states in the low-temperature D1 phase.
Orthotropic Piezoelectricity in 2D Nanocellulose
NASA Astrophysics Data System (ADS)
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-10-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V‑1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
Orthotropic Piezoelectricity in 2D Nanocellulose
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-01-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V−1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies. PMID:27708364
Orthotropic Piezoelectricity in 2D Nanocellulose.
García, Y; Ruiz-Blanco, Yasser B; Marrero-Ponce, Yovani; Sotomayor-Torres, C M
2016-10-06
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V(-1), ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
2D microwave imaging reflectometer electronics
Spear, A. G.; Domier, C. W. Hu, X.; Muscatello, C. M.; Ren, X.; Luhmann, N. C.; Tobias, B. J.
2014-11-15
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Large Area Synthesis of 2D Materials
NASA Astrophysics Data System (ADS)
Vogel, Eric
Transition metal dichalcogenides (TMDs) have generated significant interest for numerous applications including sensors, flexible electronics, heterostructures and optoelectronics due to their interesting, thickness-dependent properties. Despite recent progress, the synthesis of high-quality and highly uniform TMDs on a large scale is still a challenge. In this talk, synthesis routes for WSe2 and MoS2 that achieve monolayer thickness uniformity across large area substrates with electrical properties equivalent to geological crystals will be described. Controlled doping of 2D semiconductors is also critically required. However, methods established for conventional semiconductors, such as ion implantation, are not easily applicable to 2D materials because of their atomically thin structure. Redox-active molecular dopants will be demonstrated which provide large changes in carrier density and workfunction through the choice of dopant, treatment time, and the solution concentration. Finally, several applications of these large-area, uniform 2D materials will be described including heterostructures, biosensors and strain sensors.
2D microwave imaging reflectometer electronics.
Spear, A G; Domier, C W; Hu, X; Muscatello, C M; Ren, X; Tobias, B J; Luhmann, N C
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Assessing 2D electrophoretic mobility spectroscopy (2D MOSY) for analytical applications.
Fang, Yuan; Yushmanov, Pavel V; Furó, István
2016-12-08
Electrophoretic displacement of charged entity phase modulates the spectrum acquired in electrophoretic NMR experiments, and this modulation can be presented via 2D FT as 2D mobility spectroscopy (MOSY) spectra. We compare in various mixed solutions the chemical selectivity provided by 2D MOSY spectra with that provided by 2D diffusion-ordered spectroscopy (DOSY) spectra and demonstrate, under the conditions explored, a superior performance of the former method. 2D MOSY compares also favourably with closely related LC-NMR methods. The shape of 2D MOSY spectra in complex mixtures is strongly modulated by the pH of the sample, a feature that has potential for areas such as in drug discovery and metabolomics. Copyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd. StartCopTextCopyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd.
The ultra-violet question in maximally supersymmetric field theories
NASA Astrophysics Data System (ADS)
Bossard, G.; Howe, P. S.; Stelle, K. S.
2009-04-01
We discuss various approaches to the problem of determining which supersymmetric invariants are permitted as counterterms in maximally supersymmetric super Yang-Mills and supergravity theories in various dimensions. We review the superspace non-renormalisation theorems based on conventional, light-cone, harmonic and certain non-Lorentz covariant superspaces, and we write down explicitly the relevant invariants. While the first two types of superspace admit the possibility of one-half BPS counterterms, of the form F 4 and R 4 respectively, the last two do not. This suggests that UV divergences begin with one-quarter BPS counterterms, i.e. d 2 F 4 and d 4 R 4, and this is supported by an entirely different approach based on algebraic renormalisation. The algebraic formalism is discussed for non-renormalisable theories and it is shown how the allowable supersymmetric counterterms can be determined via cohomological methods. These results are in agreement with all the explicit computations that have been carried out to date. In particular, they suggest that maximal supergravity is likely to diverge at four loops in D = 5 and at five loops in D = 4, unless other infinity suppression mechanisms not involving supersymmetry or gauge invariance are at work.
2D Distributed Sensing Via TDR
2007-11-02
plate VEGF CompositeSensor Experimental Setup Air 279 mm 61 78 VARTM profile: slope RTM profile: rectangle 22 1 Jul 2003© 2003 University of Delaware...2003 University of Delaware All rights reserved Vision: Non-contact 2D sensing ü VARTM setup constructed within TL can be sensed by its EM field: 2D...300.0 mm/ns. 1 2 1 Jul 2003© 2003 University of Delaware All rights reserved Model Validation “ RTM Flow” TDR Response to 139 mm VEGC
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials.
Light-cone analysis of ungauged and topologically gauged BLG theories
NASA Astrophysics Data System (ADS)
Nilsson, Bengt E. W.
2009-09-01
We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in Gran and Nilsson (2009 J. High Energy Phys. JHEP03(2009)074 (arXiv:0809.4478 [hep-th]))) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG light-cone theory looks more conventional and, apart from the order of the interaction terms, resembles \\mathcal N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given at the quadratic order together with a suggested form for the quartic terms. Some problems with constructing the sixth-order interaction terms are also discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons-type terms of \\mathcal N=8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.
Marginal fluctuations as instantons on M2/D2-branes
NASA Astrophysics Data System (ADS)
Naghdi, M.
2014-03-01
We introduce some (anti-) M/D-branes through turning on the corresponding field strengths of the 11- and 10-dimensional supergravity theories over spaces, where we use and for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of the Aharony-Bergman-Jafferis-Maldacena model, all symmetries and supersymmetries are preserved trivially. In this case, we obtain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of and , and it agrees with a marginal boundary operator of the conformal dimension of . However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no back-reaction. The resultant theory now breaks all supersymmetries to , while the other symmetries are so preserved. The dual boundary operator is then set up from the skew-whiffing of the representations and for the supercharges and scalars, respectively, while the fermions remain fixed in of the original theory. Besides, we also address another alternate bulk to boundary matching procedure through turning on one of the gauge fields of the full gauge group along the same lines with a similar situation to the one faced in the AdS/CFT correspondence. The latter approach covers the difficulty already faced with in the bulk-boundary matching procedure for as well.
Parallel Stitching of 2D Materials.
Ling, Xi; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L; Bie, Yaqing; Lee, Yi-Hsien; Zhu, Yimei; Wu, Lijun; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomás; Kong, Jing
2016-03-23
Diverse parallel stitched 2D heterostructures, including metal-semiconductor, semiconductor-semiconductor, and insulator-semiconductor, are synthesized directly through selective "sowing" of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. The methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Beckett, Phil
2012-01-01
The technique of two-dimensional (2D) gel electrophoresis is a powerful tool for separating complex mixtures of proteins, but since its inception in the mid 1970s, it acquired the stigma of being a very difficult application to master and was generally used to its best effect by experts. The introduction of commercially available immobilized pH gradients in the early 1990s provided enhanced reproducibility and easier protocols, leading to a pronounced increase in popularity of the technique. However gel-to-gel variation was still difficult to control without the use of technical replicates. In the mid 1990s (at the same time as the birth of "proteomics"), the concept of multiplexing fluorescently labeled proteins for 2D gel separation was realized by Jon Minden's group and has led to the ability to design experiments to virtually eliminate gel-to-gel variation, resulting in biological replicates being used for statistical analysis with the ability to detect very small changes in relative protein abundance. This technology is referred to as 2D difference gel electrophoresis (2D DIGE).
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; ...
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Topological Quantum Field Theory and the Geometric Langlands Correspondence
NASA Astrophysics Data System (ADS)
Setter, Kevin
In the pioneering work of A. Kapustin and E. Witten, the geometric Langlands program of number theory was shown to be intimately related to duality of GL-twisted N = 4 super Yang-Mills theory compactified on a Riemann surface. In this thesis, we generalize Kapustin-Witten by investigating compactification of the GL-twisted theory to three dimensions on a circle (for various values of the twisting parameter t). By considering boundary conditions in the three-dimensional description, we classify codimension-two surface operators of the GL-twisted theory, generalizing those surface operators studied by S. Gukov and E. Witten. For t = i, we propose a complete description of the 2-category of surface operators in terms of module categories, and, in addition, we determine the monoidal category of line operators which includes Wilson lines as special objects. For t = 1 and t = 0, we discuss surface and line operators in the abelian case. We generalize Kapustin-Witten also by analyzing a separate twisted version of N = 4, the Vafa-Witten theory. After introducing a new four-dimensional topological gauge theory, the gauged 4d A-model, we locate the Vafa-Witten theory as a special case. Compactification of the Vafa-Witten theory on a circle and on a Riemann surface is discussed. Several novel two- and three-dimensional topological gauge theories are studied throughout the thesis and in the appendices. In work unrelated to the main thread of the thesis, we conclude by classifying codimension-one topological defects in two-dimensional sigma models with various amounts of supersymmetry.
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct “beyond graphene” domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology.
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-02-06
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct "beyond graphene" domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials.
Introduction to gauge theories of the strong, weak, and electromagnetic interactions
Quigg, C.
1980-07-01
The plan of these notes is as follows. Chapter 1 is devoted to a brief evocative review of current beliefs and prejudices that form the context for the discussion to follow. The idea of Gauge Invariance is introduced in Chapter 2, and the connection between conservation laws and symmetries of the Lagrangian is recalled. Non-Abelian gauge field theories are constructed in Chapter 3, by analogy with the familiar case of electromagnetism. The Yang-Mills theory based upon isospin symmetry is constructed explicitly, and the generalization is made to other gauge groups. Chapter 4 is concerned with spontaneous symmetry breaking and the phenomena that occur in the presence or absence of local gauge symmetries. The existence of massless scalar fields (Goldstone particles) and their metamorphosis by means of the Higgs mechanism are illustrated by simple examples. The Weinberg-Salam model is presented in Chapter 5, and a brief resume of applications to experiment is given. Quantum Chromodynamics, the gauge theory of colored quarks and gluons, is developed in Chapter 6. Asymptotic freedom is derived schematically, and a few simple applications of perturbative QCD ae exhibited. Details of the conjectured confinement mechanism are omitted. The strategy of grand unified theories of the strong, weak, and electromagnetic interactions is laid out in Chapter 7. Some properties and consequences of the minimal unifying group SU(5) are presented, and the gauge hierarchy problem is introduced in passing. The final chapter contains an essay on the current outlook: aspirations, unanswered questions, and bold scenarios.
Screening and transport in 2D semiconductor systems at low temperatures.
Das Sarma, S; Hwang, E H
2015-11-17
Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover.
Screening and transport in 2D semiconductor systems at low temperatures
Das Sarma, S.; Hwang, E. H.
2015-01-01
Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover. PMID:26572738
Compatible embedding for 2D shape animation.
Baxter, William V; Barla, Pascal; Anjyo, Ken-Ichi
2009-01-01
We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, and is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually motivated principles of scale-space and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes' interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work.
Schottky diodes from 2D germanane
NASA Astrophysics Data System (ADS)
Sahoo, Nanda Gopal; Esteves, Richard J.; Punetha, Vinay Deep; Pestov, Dmitry; Arachchige, Indika U.; McLeskey, James T.
2016-07-01
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe2 framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Extrinsic Cation Selectivity of 2D Membranes
2017-01-01
From a systematic study of the concentration driven diffusion of positive and negative ions across porous 2D membranes of graphene and hexagonal boron nitride (h-BN), we prove their cation selectivity. Using the current–voltage characteristics of graphene and h-BN monolayers separating reservoirs of different salt concentrations, we calculate the reversal potential as a measure of selectivity. We tune the Debye screening length by exchanging the salt concentrations and demonstrate that negative surface charge gives rise to cation selectivity. Surprisingly, h-BN and graphene membranes show similar characteristics, strongly suggesting a common origin of selectivity in aqueous solvents. For the first time, we demonstrate that the cation flux can be increased by using ozone to create additional pores in graphene while maintaining excellent selectivity. We discuss opportunities to exploit our scalable method to use 2D membranes for applications including osmotic power conversion. PMID:28157333
Static & Dynamic Response of 2D Solids
Lin, Jerry
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surface contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.
Explicit 2-D Hydrodynamic FEM Program
Lin, Jerry
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.