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.
Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory
Ydri, Badis
2007-05-15
We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two plaquettes. This equivalence holds in the 'fuzzy sphere' phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the matrix phase we have a U(N) gauge theory on a single point.
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-04-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU( N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D = 4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D > 2.
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.
Duality in supersymmetric Yang-Mills theory
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Curving Yang-Mills-Higgs gauge theories
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2015-10-01
We present a Yang-Mills-Higgs (YMH) gauge theory in which structure constants of the gauge group may depend on Higgs fields. The data of the theory are encoded in the bundle E →M , where the base M is the target space of Higgs fields and fibers carry information on the gauge group. M is equipped with a metric g and E carries a connection ∇. If ∇ is flat, R∇=0 , there is a local field redefinition which gives back the standard YMH gauge theory. If R∇≠0 , one obtains a new class of gauge theories. In this case, contrary to the standard wisdom of the YMH theory, the space (M ,g ) may have no isometries. We build a simple example which illustrates this statement.
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.
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.
Yang-Mills Theory and Fermionic Path Integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In my talk I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this talk are mostly pedagogical except for a recent analysis of path integral bosonization.
Yang-Mills theory and fermionic path integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-01-01
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.
Center vortex model for Sp(2) Yang-Mills theory
Engelhardt, M.; Sperisen, B.
2006-12-15
The question whether the center vortex picture of the strongly interacting vacuum can encompass the infrared dynamics of both SU(2) as well as Sp(2) Yang-Mills theory is addressed. These two theories contain the same center vortex degrees of freedom, and yet exhibit deconfinement phase transitions of different order. This is argued to be caused by the effective action governing the vortices being different in the two cases. To buttress this argument, a random vortex world-surface model is constructed which reproduces available lattice data characterizing Sp(2) Yang-Mills confinement properties. A new effective action term which can be interpreted in terms of a vortex stickiness serves to realize a first-order deconfinement phase transition, as found in Sp(2) Yang-Mills theory. Predictions are given for the behavior of the spatial string tension at finite temperatures.
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.
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.
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...
On matrix model formulations of noncommutative Yang-Mills theories
Azeyanagi, Tatsuo; Hirata, Tomoyoshi; Hanada, Masanori
2008-11-15
We study the stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to the noncommutative Yang-Mills theories. It turns out that most noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R{sup D} pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic noncommutative Yang-Mills theories are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.
A superspace formulation of Yang-Mills theory on sphere
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Deguchi, Shinichi
2010-05-01
A superspace approach to the Becchi-Rouet-Stora-Tyutin (BRST) formalism for the Yang-Mills theory on an n-dimensional unit sphere S1n is developed in a manifestly covariant manner based on the rotational supersymmetry characterized by the supergroup OSp(n +1∣2). This is done by employing an (n +2)-dimensional unit supersphere S1n∣2 parametrized by n commutative and two anticommutative coordinate variables so that it includes S1n as a subspace and realizes the OSp(n +1∣2) supersymmetry. In this superspace formulation, referred to as the supersphere formulation, the so-called horizontality condition is concisely expressed in terms of the rank-3 field strength tensor of a Yang-Mills superfield on S1n∣2. The supersphere formulation completely covers the BRST gauge-fixing procedure for the Yang-Mills theory on S1n provided by us [R. Banerjee and S. Deguchi, Phys. Lett. B 632, 579 (2006); arXiv:hep-th/0509161]. Furthermore, this formulation admits the (massive) Curci-Ferrari model defined on S1n, describing the gauge-fixing and mass terms on S1n together as a mass term on S1n∣2.
Yang-Mills theories at high energy accelerators
NASA Astrophysics Data System (ADS)
Sterman, George
2016-03-01
I will begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
Yang-Mills Theories at High Energy Accelerators
NASA Astrophysics Data System (ADS)
Sterman, George
I will begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
Ward identity implies recursion relations in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chen, Gang
2012-07-01
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Fermion actions extracted from lattice super Yang-Mills theories
NASA Astrophysics Data System (ADS)
Misumi, Tatsuhiro
2013-12-01
We revisit 2D = (2, 2) super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-U(1) R symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two manners: (1) pseudo-8D sixteen-spinor treatment of 4D four flavors with eight 8D gamma matrices, (2) pseudo-6D eight-spinor treatment of 4D two flavors with five out of six 6D gamma matrices. We obtain 4D four-species and two-species lattice fermions with unbroken subgroup of chiral symmetry and other essential properties. We discuss their relations to staggered and Wilson twisted-mass fermions. We also discuss their potential feedback to 4D super Yang-Mills lattice formulations.
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.
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. PMID:26406822
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.
Solvable relativistic hydrogenlike system in supersymmetric Yang-Mills theory.
Caron-Huot, Simon; Henn, Johannes M
2014-10-17
The classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N = 4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling. PMID:25361249
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.
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.
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.
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.
Dual superconductivity and vacuum properties in Yang Mills theories
NASA Astrophysics Data System (ADS)
D'Alessandro, A.; D'Elia, M.; Tagliacozzo, L.
2007-07-01
We address, within the dual superconductivity model for color confinement, the question whether the Yang-Mills vacuum behaves as a superconductor of type I or type II. In order to do that we compare, for the theory with gauge group SU(2), the determination of the field penetration depth λ with that of the superconductor correlation length ξ. The latter is obtained by measuring the temporal correlator of a disorder parameter developed by the Pisa group to detect dual superconductivity. The comparison places the vacuum close to the border between type I and type II and marginally on the type II side. We also check our results against the study of directly measurable effects such as the interaction between two parallel flux tubes, obtaining consistent indications for a weak repulsive behaviour. Future strategies to improve our investigation are discussed.
A euclidean lattice formulation of D = 5 maximally supersymmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Joseph, Anosh
2016-06-01
We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known gravitational dual.
Thierry-Mieg, J.
1985-05-14
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity.
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.
Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories
Golterman, Maarten; Zimmerman, Leah
2005-06-01
We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result.
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.
Towards the fundamental spectrum of the quantum Yang-Mills theory
NASA Astrophysics Data System (ADS)
Liegener, Klaus; Thiemann, Thomas
2016-07-01
In this work we focus on the quantum Einstein-Yang-Mills sector quantized by the methods of loop quantum gravity. We point out the improved UV behavior of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact with the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relationship of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.
String theories as the adiabatic limit of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Popov, Alexander D.
2015-08-01
We consider Yang-Mills theory with a matrix gauge group G on a direct product manifold M =Σ2×H2 , where Σ2 is a two-dimensional Lorentzian manifold and H2 is a two-dimensional open disc with the boundary S1=∂H2 . The Euler-Lagrange equations for the metric on Σ2 yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on H2 is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a world sheet Σ2 moving in the based loop group Ω G =C∞(S1,G )/G , where S1 is the boundary of H2. By choosing G =Rd -1 ,1 and putting to zero all parameters in Ω Rd -1 ,1 besides Rd -1 ,1 , we get a string moving in Rd -1 ,1 . In another paper of the author, it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on Σ2×H2 while H2 shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold Σ2×S1 and show that in the limit when the radius of S1 tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.
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.
Karanikas, A.I.; Ktorides, C.N.
1987-02-15
We confront the general problem posed by nonperturbative calculations in non-Abelian gauge theories, pertaining to the Wilson loop operator, away from strong coupling. We adopt a nonperturbatively regularized formulation of Yang-Mills theories in the continuum which has already been discussed in the preceding paper. We study, in particular, Yang-Mills duality, within our regularized context, with respect to the full SU(N) group and not simply its center Z/sub N/. We further show that, from the present viewpoint, duality emerges through a distinction between the regularization length on one hand and the scale by which the Yang-Mills system is observed on the other. Finally, we are able to derive a Makeenko-Migdal-type equation for finite N.
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.
Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge—Revisited
NASA Astrophysics Data System (ADS)
Reinhardt, Hugo; Campagnari, Davide R.; Leder, Markus; Burgio, Giuseppe; Pawlowski, Jan M.; Quandt, Markus; Weber, Axel
2011-05-01
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.
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.
Yang-Mills Gauge Theory and the Higgs Boson Family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09±0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
Yang-Mills gauge theory and the Higgs boson family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
2016-01-01
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09 ± 0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
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.
Real-time dynamics of a hot Yang-Mills theory: a numerical analysis
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Krasnitz, A.
2002-03-01
We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.
Real-time dynamics of a hot Yang-Mills theory: a numerical analysis
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Krasnitz, A.
We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.
Explicit non-Abelian monopoles and instantons in SU(N) pure Yang-Mills theory
Popov, Alexander D.
2008-06-15
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R{sup 3,1}. I show that such solutions exist in SU(N) gauge theory on the spaces R{sup 2}xS{sup 2} and RxS{sup 1}xS{sup 2} with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on TxS{sup 2}, where T is R or S{sup 1}. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the {phi}{sup 4} kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R{sup 1,1}xS{sup 2} via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on RxS{sup 1} admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S{sup 1} with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space RxS{sup 1}xS{sup 2} which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S{sup 1}xS{sup 3} interpreted as chains of n instanton-anti-instanton pairs.
Isotropy theorem for cosmological Yang-Mills theories
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2013-02-01
We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills field is always isotropic and has the perfect fluid form for any locally inertial observer.
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.
Kuerkcueoglu, Seckin
2010-11-15
We consider a U(2) Yang-Mills theory on MxS{sub F}{sup 2}, where M is an arbitrary noncommutative manifold, and S{sub F}{sup 2} is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in [D. Harland and S. Kurkcuoglu, Nucl. Phys. B 821, 380 (2009).], we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane M=R{sub {theta}}{sup 2} and find that, in certain limits, it admits noncommutative, non-Bogomol'nyi-Prasad-Somerfield vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.
PP-wave string interactions from perturbative Yang-Mills theory
NASA Astrophysics Data System (ADS)
Constable, Neil R.; Freedman, Daniel Z.; Headrick, Matthew; Minwalla, Shiraz; Motl, Lubos; Postnikov, Alexander; Skiba, Witold
2002-07-01
Recently, Berenstein et al. have proposed a duality between a sector of Script N = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be λ' = gYM2N/J2 = 1/(μp+α')2. We study Yang-Mills theory at small λ' (large μ) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4πgs)2(μp+α')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(λ')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and λ' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.
Variational Approach to Yang-Mills Theory with non-Gaussian Wave Functionals
NASA Astrophysics Data System (ADS)
Campagnari, Davide R.; Reinhardt, Hugo
2011-05-01
A general method for treating non-Gaussian wave functionals in quantum field theory is presented and applied to the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in order to include a three-gluon kernel in the exponential of the vacuum wave functional. The three-gluon vertex is calculated using the propagators found in the variational approach with a Gaussian trial wave functional as input.
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.
Yangian symmetry of smooth Wilson loops in super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Müller, Dennis; Münkler, Hagen; Plefka, Jan; Pollok, Jonas; Zarembo, Konstantin
2013-11-01
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in super Yang-Mills theory are invariant under a Yangian symmetry Y [(2, 2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS5 × S 5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the super Yang-Mills theory.
On Twisted N = 2 5D Super Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Qiu, Jian; Zabzine, Maxim
2016-01-01
On a five-dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys-Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa-Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys-Witten equations on product manifolds {M_5 = M_4 × R} arise in the context of twisting the 5D maximally supersymmetric Yang-Mills theory. In this paper, we present the construction of twisted N = 2 Yang-Mills theory on Sasaki-Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys-Witten equation.
Physical unitarity for a massive Yang-Mills theory without the Higgs field: A perturbative treatment
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Suzuki, Kenta; Fukamachi, Hitoshi; Nishino, Shogo; Shinohara, Toru
2013-01-01
In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
Lim, Kok-Geng; Teh, Rosy
2010-07-07
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter {epsilon} {ne} 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter {epsilon} {yields} 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
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.
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}
Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Emmenegger, N.
2001-11-01
In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.
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)
Euclidean wormhole solutions of Einstein-Yang-Mills theory in diverse dimensions
Yoshida, K.; Hirenzaki, S. ); Shiraishi, K. )
1990-09-15
We solve the Euclidean Einstein equations with non-Abelian gauge fields of sufficiently large symmetry in various dimensions. In higher-dimensional spaces, we find the solutions which are similar to so-called scalar wormholes. In four-dimensional space-time, we find singular wormhole solutions with infinite Euclidean action. Wormhole solutions in the three-dimensional Einstein-Yang-Mills theory with a Chern-Simons term are also constructed.
NASA Astrophysics Data System (ADS)
Bassetto, Antonio; DePol, Giancarlo; Torrielli, Alessandro; Vian, Federica
2005-05-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling
NASA Astrophysics Data System (ADS)
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2010-05-01
We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.
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. PMID:25763951
Yang-Mills Theory at 60: Milestones, Landmarks and Interesting Questions
NASA Astrophysics Data System (ADS)
Chau, Ling-Lie
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 are worthy of answers from future researches. The paper is written (without equations) for the interest of non-scientists as well as of scientists.
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.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506
Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2010-05-28
We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.
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.
N=4 supersymmetric Yang-Mills theory in soft-collinear effective theory
Chay, Junegone; Lee, Jae Yong
2011-01-01
We formulate N=4 supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter {eta}{approx}p{sub perpendicular}/Q. All the particles in this theory are in the adjoint representation of the SU(N) gauge group, and we derive the collinear gauge-invariant Lagrangian in the adjoint and fundamental representations, respectively. We consider collinear and ultrasoft Wilson lines in this theory, and show the ultrasoft factorization of the collinear Lagrangian by redefining the collinear fields with the use of the ultrasoft Wilson lines. The vertex correction for a vector fermion current at one loop is explicitly presented as an example to illustrate how the computation is performed in the effective theory.
Gauss' law and nonlinear plane waves for Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
The Hamiltonian analysis for Yang-Mills theory on R×S
NASA Astrophysics Data System (ADS)
Agarwal, Abhishek; Nair, V. P.
2009-07-01
Pure Yang-Mills theory on R×S is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on R. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on R in the limit in which the sphere is de-compactified to a plane.
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. PMID:25166817
Five-Loop Four-Point Amplitude of N=4 Super-Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Bern, Z.; Carrasco, J. J. M.; Johansson, H.; Roiban, R.
2012-12-01
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N=8 supergravity required to resolve the general ultraviolet behavior of supergravity theories.
On the deconfining limit in (2+1)-dimensional Yang-Mills theory
NASA Astrophysics Data System (ADS)
Abe, Yasuhiro
2010-03-01
We consider (2+1)-dimensional Yang-Mills theory on S×S×R in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the S radii of the torus ( S×S), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.
Gravity and Yang-Mills Amplitude Relations in Field Theory
NASA Astrophysics Data System (ADS)
Søndergaard, Thomas
2011-07-01
We review some recent work in the famous Kawai-Lewellen-Tye (KLT) relations. Especially we present a compact way of writing down the general n-point relation. We also look at an extra feature of these relations which were only very recently realized, and leads to new relations among gauge-theory amplitudes.
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.
Lower Dimension Vacuum Defects in Lattice Yang-Mills Theory
Zakharov, V.I.
2005-04-01
We overview lattice data on d = 0, 1, 2, 3 dimensional vacuum defects in lattice four-dimensional SU(2) (SU(3)) gluodynamics. In all the cases, defects have a total volume which scales in physical units (with zero fractal dimension). In the case of d = 1, 2, the defects are distinguished by ultraviolet divergent non-Abelian action as well. This sensitivity to the ultraviolet scale allows us to derive strong constraints from the continuum theory on the properties of the defects, which turn out to be satisfied by the lattice data. We discuss a classification scheme of the defects which allows us to (at least) visualize the defect properties in a simple and unified way. A not-yet-checked relation of the defects to the spontaneous chiral symmetry breaking is suggested by the scheme. Finally, we present some arguments that the defects considered could become fundamental variables of a dual formulation of the theory.
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.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
Nonperturbative gluon and ghost propagators for d=3 Yang-Mills theory
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2010-06-15
We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in d=3 Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in d=3), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of SU(2) lattice simulations.
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. PMID:19518940
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.
Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
NASA Astrophysics Data System (ADS)
de Medeiros, Paul; Figueroa-O'Farrill, José
2016-03-01
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.
Composite Operators in the Twistor Formulation of N =4 Supersymmetric Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Koster, Laura; Mitev, Vladimir; Staudacher, Matthias; Wilhelm, Matthias
2016-07-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of N =4 super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this Letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper.
Composite Operators in the Twistor Formulation of N=4 Supersymmetric Yang-Mills Theory.
Koster, Laura; Mitev, Vladimir; Staudacher, Matthias; Wilhelm, Matthias
2016-07-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of N=4 super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this Letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper. PMID:27419558
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O'Connell, Donal
2015-10-01
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.
Towards a consistent noncommutative supersymmetric Yang-Mills theory: Superfield covariant analysis
Ferrari, A.F.; Girotti, H.O.; Ribeiro, A.A.; Gomes, M.; Rivelles, V.O.; Silva, A.J. da; Petrov, A.Yu.
2004-10-15
Commutative four dimensional supersymmetric Yang-Mills (SYM) theory is known to be renormalizable for N=1,2, and finite for N=4. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the N=1,2,4 noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield V. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the V superfield exhibits UV divergences. They are found to cancel, in the Feynman gauge, for the maximally extended N=4 supersymmetric theory. This gives support to the belief that the N=4 NCSYM theory is UV finite.
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.
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele; Young, Donovan
2015-10-01
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S matrix of N=4 super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi, and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S matrix of N=4 super Yang-Mills theory implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator. PMID:26551805
Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Reinhardt, H.; Campagnari, D.; Heffner, J.
2014-04-01
Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU(N) Yang-Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).
Yangian symmetry of scattering amplitudes in Script N = 4 super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Drummond, James; Henn, Johannes; Plefka, Jan
2009-05-01
Tree-level scattering amplitudes in Script N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar Script N = 4 super Yang-Mills, at least at tree level.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo
2015-10-01
We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02χ =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the θ behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.
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.
Complex time solutions with nontrivial topology and multiparticle scattering in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Gould, Thomas M.; R. Poppitz, Erich
1993-08-01
A classical solution in Yang-Mills thoery is given a new semiclassical interpretation in terms of particle scattering. It solves the complex time boundary value problem which arises in the semiclassical approximation to a multiparticle transition probability in the one-instanton sector at fixed energy. The imaginary part of the action of the solution on the complex time contour and its topological charge obey the same relation as the self-dual Euclidean configurations. Hence the solution is relevant for the problem of tunneling with fermion number violation in the electroweak theory. It describes transitions from an initial state with a smaller number of particles to a final state with a larger umber of particles. The implications of these results for multiparticle production in the electroweak theory are also discussed.
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_{5} x S;{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_{4}/three-dimensional conformal field theory duality is also treated in a similar fashion. PMID:19905502
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.
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
NASA Astrophysics Data System (ADS)
Hofmann, Ralf
2014-04-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (anti)selfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anti)calorons of scale parameter ρ ˜ |φ|-1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anti)caloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anti)caloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in
Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Huber, Markus Q.
2016-04-01
The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the three-particle irreducible effective action. Within a self-contained truncation, various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.
Thermal monopole condensation and confinement in finite temperature Yang-Mills theories
D'Alessandro, Alessio; D'Elia, Massimo; Shuryak, Edward V.
2010-05-01
We investigate the connection between color confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular, we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensation of such objects happening right at the deconfining transition. We also address the question of the thermal monopole mass, showing that different definitions give consistent results only around the transition, where the monopole mass goes down and becomes of the order of the critical temperature itself.
Symmetries of the 4D self-dual Yang-Mills equation and the reduction to the 2D KdV equation
HoSeong La )
1992-04-01
The Lie-point and the Lie-Baecklund symmetries of 4D self-dual Yang-Mills equation are investigated as those of differential equations. The Lie-point symmetry is nothing but the gauge symmetry at the level of field equation, but the Lie-Baecklund symmetries are new. In particular, by the symmetry reduction to KdV equation in 2D the corresponding Lie-Baecklund symmetries which reduce to the isospectral symmetries or to the nonisospectral symmetries are identified. Some speculations on the existence of the self-dual Yang-Mills hierarchy as well as the derivation of the 4D analogue of the string equation of the nonperturbative 2D quantum gravity are given.
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Pérez, Margarita García; González-Arroyo, Antonio; Okawa, Masanori
2013-09-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λ N L and an angle defined in terms of the magnetic flux (λ is `t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence ( N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
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
Cucchieri, A.; Mendes, T.
2008-11-01
We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p{sup -2-2{kappa}} with {kappa}{approx_equal}0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.
Analytical study of Yang-Mills theory in the infrared from first principles
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2016-06-01
Pure Yang-Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the coupling becomes small and the one-loop approximation is under full control.
Plane-wave matrix theory from N=4 super-Yang-Mills on R×S 3
NASA Astrophysics Data System (ADS)
Kim, Nakwoo; Klose, Thomas; Plefka, Jan
2003-11-01
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
NASA Astrophysics Data System (ADS)
Bergner, G.; Langelage, J.; Philipsen, O.
2015-11-01
We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling β c is reproduced to better than one percent from a one-coupling effective theory on N τ = 4 lattices while up to five couplings are needed on N τ = 8 for the same accuracy.
Massive Yang-Mills theory based on the nonlinearly realized gauge group
Bettinelli, D.; Ferrari, R.; Quadri, A.
2008-02-15
We propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group [here SU(2)]. It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops, and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts, and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak-power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2){sub L} local x SU(2){sub R} global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
Yang-Mills field theory in an axial field-strength gauge
NASA Astrophysics Data System (ADS)
Tyburski, Lawrence
1984-02-01
We introduce what we call an axial field-strength gauge as an alternative to the conventional Coulomb gauge in the Yang-Mills field theory. This new gauge does not share the pathologies that were shown to exist in the Coulomb gauge by Gribov and Mandelstam. We apply this new gauge to the calculation, in two special cases, of the energy possessed by sources J1,20 interacting in the presence of a background field produced by a source J30, which is assumed to be of order g-1, in the limit g goes to zero, where g is the coupling constant. In the case in which the charge density J30 consists of two infinite uniform parallel plates bearing charge densities equal in magnitude but opposite in sign, we find that the potential energy possessed by two point particles bearing charge densities J1,20 grows linearly in proportion to the distance between them at large distances when the two particles are separated along a line parallel to the background field. This is a confining potential.
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.
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.
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.
The Two-Loop Six-Point MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C.; Volovich, A.
2008-03-12
We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N = 4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.
An object oriented code for simulating supersymmetric Yang-Mills theories
NASA Astrophysics Data System (ADS)
Catterall, Simon; Joseph, Anosh
2012-06-01
We present SUSY_LATTICE - a C++ program that can be used to simulate certain classes of supersymmetric Yang-Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space-time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space-time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and N=4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICE Catalogue identifier: AELS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9315 No. of bytes in distributed program
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.
Gauging Quantum Groups: Yang-Baxter Joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Gauging quantum groups: Yang-Baxter joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
2016-02-01
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L. )
1991-02-15
We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.
Bonus Yangian Symmetry for the Planar S Matrix of N=4 Supersymmetric Yang-Mills Theory
Beisert, Niklas; Schwab, Burkhard U. W.
2011-06-10
Recent developments in the determination of the planar S matrix of N=4 super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.
Self-dual solutions of Yang-Mills theory on Euclidean AdS space
Sarioglu, Oezguer; Tekin, Bayram
2009-05-15
We find nontrivial, time-dependent solutions of the (anti) self-dual Yang-Mills equations in the four-dimensional Euclidean anti-de Sitter space. In contrast to the Euclidean flat space, the action depends on the moduli parameters and the charge can take any noninteger value.
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.
Kovtun, Pavel; Uensal, Mithat; Yaffe, Laurence G.
2005-11-15
In previous work, we found that necessary and sufficient conditions for large N{sub c} equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N{sub c}) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z{sub k} projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z{sub k} projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N{sub c} equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z{sub 2} projections, we show that previous assertions of large N{sub c} inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter.
Emerging geometry from maximally super-symmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Vazquez, Samuel Enrique
In this thesis, we explore the emergence of space-time geometry, and string theory physics from N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group U(N). This is done in the context of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT). The main results of this thesis are the following. First, we study single trace perturbations around generic 1/2 BPS states of the theory. We do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show how these states can be mapped to dynamical lattices with boson statistics and periodic boundary conditions. By dynamical, we mean that the total boson occupation number is not conserved in general. Then, we show how to derive an effective sigma model for these systems which coincides with the Polyakov action of a probe string on a 1/2 BPS geometry (in the fast string limit). Secondly, we study non-supersymmetric perturbations of the vacuum which give rise to bosonic lattices with open boundary conditions. We also do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show that these states are dual to open strings on D3-branes known as "Giant Gravitons". These lattice systems are also dynamical, but in some special cases, we show that we get an integrable spin chain with open boundary conditions. Next, we study single trace perturbations at strong coupling. We do this by taking a "dilute gas" approximation. We derive an all-loop result for the dispersion relation of the "magnons" which coincides with previous conjectures in the literature. What is more, we derive the geometrical picture of the so-called "giant magnon" string solution of Hofman and Maldacena, directly from the field theory. Finally, we explore the question of classical integrability of open strings on D-branes. In particular, we study the case of the giant gravitons, and compare the integrable structures on both sides of the AdS/CFT correspondence.
Classical Yang-Mills Theory with Fermions II:. DIRAC’S Observables
NASA Astrophysics Data System (ADS)
Lusanna, Luca
For pure Yang-Mills theory on Minkowski space-time, formulated in functional spaces where the covariant divergence is an elliptic operator without zero modes, and for a trivial principal bundle over the fixed time Euclidean space with a compact, semisimple, connected and simply connected structure Lie group, a Green function for the covariant divergence has been found. It allows one to solve the first class constraints associated with Gauss’ laws and to identify a connection-dependent coordinatization of the trivial principal bundle. In a neighborhood of the global identity section, by using canonical coordinates of the first kind on the fibers, one has a symplectic implementation of the Lie algebra of the small gauge transformations generated by Gauss’ laws and one can make a generalized Hodge decomposition of the gauge potential one-forms based on the BRST operator. This decomposition singles out a pure gauge background connection (the BRST ghost as Maurer-Cartan one-form on the group of gauge transformations) and a transverse gauge-covariant magnetic gauge potential. After an analogous decomposition of the electric field strength into the transverse and the longitudinal part, Dirac’s observables associated with the transverse electric and magnetic components are identified as their restriction to the global identity section of the trivial principal bundle. The longitudinal part of the electric field can be re-expressed in terms of these electric and magnetic transverse parts and of the constraints without Gribov ambiguity. The physical Lagrangian, Hamiltonian, non-Abelian and topological charges have been obtained in terms of transverse Dirac’s observables, also in the presence of fermion fields, after a symplectic decoupling of the gauge degrees of freedom; one has an explicit realization of the abstract “Riemannian metric” on the orbit space. Both the Lagrangian and the Hamiltonian are nonlocal and nonpolynomial; like in the Coulomb gauge they are
Supergravitons from one loop perturbative N=4 super Yang-Mills theory
Janik, Romuald A.; Trzetrzelewski, Maciej
2008-04-15
We determine the partition function of (1/16)BPS operators in N=4 super Yang-Mills (SYM) at weak coupling at the one-loop level in the planar limit. This partition function is significantly different from the one computed at zero coupling. We find that it coincides precisely with the partition function of a gas of (1/16)BPS supergravitons in AdS{sub 5}xS{sup 5}.
The construction of dual-trace factor in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao
2013-07-01
Recently, a BCJ dual of the color-ordered formula for Yang-Mills amplitude was proposed, where the dual-trace factor satisfies cyclic symmetry and KK-relation. In this paper, we present a systematic construction of the dual-trace factor based on its proposed relations to kinematic numerators in dual-DDM form. We show that the construction presented respects relabeling symmetry. In addition, we show that using relabeling symmetry as conditions, the same construction can be solved independently.
Effective metrics in the non-minimal Einstein-Yang-Mills-Higgs theory
Balakin, A.B. Dehnen, H. Zayats, A.E.
2008-09-15
We formulate a self-consistent non-minimal five-parameter Einstein-Yang-Mills-Higgs (EYMH) model and analyse it in terms of effective (associated, color and color-acoustic) metrics. We use a formalism of constitutive tensors in order to reformulate master equations for the gauge, scalar and gravitational fields and reconstruct in the algebraic manner the so-called associated metrics for the Yang-Mills field. Using WKB-approximation we find color metrics for the Yang-Mills field and color-acoustic metric for the Higgs field in the framework of five-parameter EYMH model. Based on explicit representation of these effective metrics for the EYMH system with uniaxial symmetry, we consider cosmological applications for Bianchi-I, FLRW and de Sitter models. We focus on the analysis of the obtained expressions for velocities of propagation of longitudinal and transversal color and color-acoustic waves in a (quasi)vacuum interacting with curvature; we show that curvature coupling results in time variations of these velocities. We show, that the effective metrics can be regular or can possess singularities depending on the choice of the parameters of non-minimal coupling in the cosmological models under discussion. We consider a physical interpretation of such singularities in terms of phase velocities of color and color-acoustic waves, using the terms 'wave stopping' and 'trapped surface'.
The Types of Axisymmetric Exact Solutions Closely Related to n-SOLITONS for Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Zhong, Zai Zhe
In this letter, we point out that if a symmetric 2×2 real matrix M(ρ,z) obeys the Belinsky-Zakharov equation and |det(M)|=1, then an axisymmetric Bogomol'nyi field exact solution for the Yang-Mills-Higgs theory can be given. By using the inverse scattering technique, some special Bogomol'nyi field exact solutions, which are closely related to the true solitons, are generated. In particular, the Schwarzschild-like solution is a two-soliton-like solution.
Gao Zhifeng; Zhang Jing
2009-04-15
In this paper, we use the method of calculus of variations to establish the existence of energy-minimizing radially symmetric magnetic monopole solutions in the general (4p-1)-dimensional Yang-Mills gauge field theory developed recently by Radu and Tchrakian. We also show that these solutions are either self-dual or anti-self-dual and, hence, unique. Our study extends the existence work of Belavin, Polyakov, Schwartz, and Tyupin and the equivalence and uniqueness work of Maison in three dimensions and the work of Yang in seven dimensions to the situation of arbitrary (4p-1) dimensions.
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
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. PMID:11177888
Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation
Forkel, Hilmar
2006-05-15
We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schroedinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.
Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories
NASA Astrophysics Data System (ADS)
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2014-11-01
We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. introduction of finite BRST-antiBRST transformations, being polynomial in powers of a constant Sp(2)-doublet of Grassmann-odd parameters λa and leaving the quantum action of the Yang-Mills theory invariant to all orders in λa; definition of finite field-dependent BRST-antiBRST transformations, being polynomial in powers of an Sp(2)-doublet of Grassmann-odd functionals λa(ϕ) depending on the classical Yang-Mills fields, the ghost
Perturbative tests for a large-N reduced model of {N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2011-11-01
We study a non-perturbative formulation of {N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
Perturbative tests for a large-N reduced model of mathcal{N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2012-02-01
We study a non-perturbative formulation of mathcal{N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
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.
Correct effective potential of supersymmetric Yang-Mills theory on M{sup 4}xS{sup 1}
Haba, Naoyuki; Takenaga, Kazunori; Yamashita, Toshifumi
2005-01-15
We study an N=1 supersymmetric Yang-Mills theory defined on M{sup 4}xS{sup 1}. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, have been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the S{sup 1} direction in the case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the M{sup 4}xS{sup 1}/Z{sub 2} case.
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. PMID:24033023
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.
Direct test of the AdS/CFT correspondence by Monte Carlo studies of super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Honda, Masazumi; Ishiki, Goro; Kim, Sang-Woo; Nishimura, Jun; Tsuchiya, Asato
2013-11-01
We perform nonperturbative studies of super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but not by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large- N limit between the SU( N) theory on R × S 3 and a one-dimensional SU( N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large- N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization for S 3 preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff Λ in R direction, are made negligible by using sufficiently large Λ.
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
NASA Astrophysics Data System (ADS)
Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.
2016-05-01
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.
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)
Silva, P. J.; Oliveira, O.
2016-06-01
The correlations between the modulus of the Polyakov loop, its phase θ , and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to θ =0 , ±2 π /3 . We find that the gluon propagator form factors associated with θ ≈0 differ quantitatively and qualitatively from those associated to θ ≈±2 π /3 . This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature Tc, the difference between the propagators associated to θ ≈0 and θ ≈±2 π /3 allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
Yang-Mills connections valued on the octonionic algebra
NASA Astrophysics Data System (ADS)
Restuccia, A.; Veiro, J. P.
2016-05-01
We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulations are the usual su(2) or u(1) Yang-Mills theories.
Phase diagram of Script N = 4 super-Yang-Mills theory with R-symmetry chemical potentials
NASA Astrophysics Data System (ADS)
Yamada, Daisuke; Yaffe, Laurence G.
2006-09-01
The phase diagram of large Nc, weakly-coupled Script N = 4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. In the zero coupling limit, a transition line in the μ-T plane is found, separating a ``confined'' phase in which the Polyakov loop has vanishing expectation value from a ``deconfined'' phase in which this order parameter is non-zero. For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc2). This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. Beyond this point, no long-lived locally stable quasi-equilibrium state exists. The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known.
Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-11-15
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Holographic Wilson loops in symmetric representations in {N} = {2}^{ast } super-Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chen-Lin, Xinyi; Dekel, Amit; Zarembo, Konstantin
2016-02-01
We construct the D3-brane solution in the holographic dual of the {N} = {2}^{ast } theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chowdhury, Abhishek; Harindranath, A.; Maiti, Jyotirmoy
2016-02-01
By relating the functional averages of a generic scalar operator in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for SU(3) lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. Numerical results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.
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...
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.
NASA Astrophysics Data System (ADS)
Roche, Ph.
2016-03-01
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, 𝔽q) and PGL(2, 𝔽q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
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.
Bourjaily, Jacob L; Heslop, Paul; Tran, Vuong-Viet
2016-05-13
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. PMID:27232016
Gravity as the square of Yang-Mills?
NASA Astrophysics Data System (ADS)
Borsten, L.; Duff, M. J.
2015-10-01
In these lectures we review how symmetries of gravitational theories may be regarded as originating from those of ‘Yang-Mills squared’. We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, p-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality. Lecture delivered by M. J. Duff.
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.
NASA Astrophysics Data System (ADS)
Baxter, J. Erik
2016-02-01
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. 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.
Geometry and dynamics of a coupled 4 D-2 D quantum field theory
NASA Astrophysics Data System (ADS)
Bolognesi, Stefano; Chatterjee, Chandrasekhar; Evslin, Jarah; Konishi, Kenichi; Ohashi, Keisuke; Seveso, Luigi
2016-01-01
Geometric and dynamical aspects of a coupled 4 D-2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D C{P}^{N-1} zeromodes associated with a nonAbelian vortex become nonnormalizable.
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)
Duarte, Anthony G.; Oliveira, Orlando; Silva, Paulo J.
2016-07-01
The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 1284 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ˜(13 fm )4 and ˜(8 fm )4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant αs(p2), as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ˜1 GeV .
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.
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.
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.
Wormhole solution in coupled Yang-Mills--axion system
Das, A. Department of Astronomy, University of Rochester, Rochester, New York 14627 ); Maharana, J. )
1990-01-15
We show that wormhole solutions arise naturally in the effective action, resulting from a heterotic string theory, in which Einstein gravity is coupled to the antisymmetric tensor and an SU(2) Yang-Mills field. The Peccei-Quinn scale in this case gets related to the string tension which is natural in any string compactification.
Dynamics of Higgs fields and a route to turbulence in the theory of SU(2) Yang-Mills fields
Lavkin, A.G.
1995-09-01
The dynamics of SU(2) Yancy-Mills (YM) fields, both free fields and fields interacting with Higgs bosons, is investigated by the Poincare surface-of-section method and the method of Lyapunov maximum exponents. As for free YM fields and YM fields interacting with a Higgs condensate, the route to turbulence in the system consisting of YM fields and Higgs particles lies through an infinite sequence of period-doubling bifurcations of the relevant phase trajectory. Prospects for future investigations in this field, such as constructing a consistent dynamical theory of second-order phase transitions on the basis of the analog between such transitions and the bifurcation transition to chaos, and taking into account the effects of the quark degrees of freedom of hadron matter and of thermal and quantum vacuum fluctuations on the scenario of the development of turbulence in the theory of YM fields, are also discussed. 14 refs., 1 fig.
(Super)Yang-Mills at finite heavy-quark density
NASA Astrophysics Data System (ADS)
Faedo, Antón F.; Kundu, Arnab; Mateos, David; Tarrío, Javier
2015-02-01
We study the gravitational duals of d-dimensional Yang-Mills theories with d ≤ 6 in the presence of an density of heavy quarks, with N the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case d = 5 yields an geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.
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.
Formation and decay of Einstein-Yang-Mills black holes
NASA Astrophysics Data System (ADS)
Rinne, Oliver
2014-12-01
We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing colored and Reissner-Nordström black holes on surfaces of constant mean curvature and analyze their perturbations. These linearly perturbed black holes are then evolved into the nonlinear regime and the masses of the final Schwarzschild black holes are computed as a function of the initial horizon radius. We compare with an information-theoretic bound on the lifetime of unstable hairy black holes derived by Hod. Finally we study critical phenomena in gravitational collapse at the threshold between different Yang-Mills vacuum states of the final Schwarzschild black holes, where the n =1 colored black hole forms the critical solution. The work of Choptuik et al. [Phys. Rev. D 60, 124011 (1999)] is extended by using a family of initial data that includes another region in parameter space where the colored black hole with the opposite sign of the Yang-Mills potential forms the critical solution. We investigate the boundary between the two regions and discover that the Reissner-Nordström solution appears as a new approximate codimension-two attractor.
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.
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 ).
Orbifold singularities, Lie algebras of the third kind (LATKes), and pure Yang-Mills with matter
NASA Astrophysics Data System (ADS)
Friedmann, Tamar
2011-02-01
We discover the unique, simple Lie algebra of the third kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is one-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism. [ {c} {The World in a Point?}{Blow-up of} C^3/Z_3| {Dynkin diagram of the LATKe}bullet {Pure Yang-Mills with matter}
Combined study of the gluon and ghost condensates and <{epsilon}{sup abc}c{sup b}c{sup c}> in Euclidean SU(2) Yang-Mills theory in the Landau gauge
Capri, M.A.L.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Dudal, D.; Verschelde, H.; Gracey, J.A.
2006-01-01
The ghost condensate <{epsilon}{sup abc}c{sup b}c{sup c}> is considered together with the gluon condensate in SU(2) Euclidean Yang-Mills theories quantized in the Landau gauge. The vacuum polarization ceases to be transverse due to the nonvanishing condensate <{epsilon}{sup abc}c{sup b}c{sup c}>. The gluon propagator itself remains transverse. By polarization effects, this ghost condensate induces then a splitting in the gluon mass parameter, which is dynamically generated through . The obtained effective masses are real when is included in the analysis. In the absence of , the already known result that the ghost condensate induces effective tachyonic masses is recovered. At the one-loop level, we find that the effective diagonal mass becomes smaller than the off-diagonal one. This might serve as an indication for some kind of Abelian dominance in the Landau gauge, similar to what happens in the maximal Abelian gauge.
Yang-Mills vacuum: An attempt of lattice loop calculus
Furmanski, W.; Kolawa, A.
1985-01-01
An attempt is made to derive and to solve the Schrodinger equation in the low energy region (vacuum, first excitation, etc.) of the Yang-Mills theory on the lattice. The complete orthonormal basis in the physical Hilbert space is constructed by classifying independent solutions of Gauss's law. Loops of electric flux are chosen as elementary variables. The loop space Hamiltonian is derived, an ansatz is made for the low energy wave functionals and the Schrodinger equation is solved in the (truncated) loop basis. The resulting physical picture for the Yang-Mills vacuum in the cross-over region is that of, still quite dilute, gas of fluctuating loops. Definite candidate for the confining force emerges: the repulsive non-abelian loop-loop interaction (rather weak but persistent) generates an effective external field (''external pressure'') prohibiting unbounded loop size fluctuations. The negative sign (repulsion) is universal for all compact groups. Preliminary numerical results, so far mainly of illustrative character, are presented. 8 refs., 22 figs.
Massive Yang-Mills model and diffractive scattering
NASA Astrophysics Data System (ADS)
Forshaw, J. R.; Papavassiliou, J.; Parrinello, C.
1999-04-01
We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. With this motivation, we perform in this model explicit calculations of S-matrix elements between quark states, at the tree level, one loop, and two loops, and discuss issues of renormalizability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalizable at one-loop order, and is only logarithmically non-renormalizable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. In addition, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analyzed at the level of the S matrix. Finally, we briefly discuss the high-energy behavior of the leading order amplitude for quark-quark elastic scattering in the diffractive region. The above analysis sets up the stage for carrying out a systematic computation of the higher order corrections to the two-gluon exchange model of the Pomeron using massive gluons inside quantum loops.
Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
NASA Astrophysics Data System (ADS)
Tolotti, Mathias; Weinzierl, Stefan
2013-07-01
The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.
Emergent 5-Dimensional Black Hole from Weakly Interacting 4-Dimensional Super Yang-Mills Gas
NASA Astrophysics Data System (ADS)
Rey, Soo-Jong
2005-12-01
We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N = 4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao ``information geometry''. In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak 't Hooft coupling.
Emergent 5-Dimensional Black Hole from Weakly Interacting 4-Dimensional Super Yang-Mills Gas
Rey, Soo-Jong
2005-12-02
We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N = 4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao 'information geometry'. In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak 't Hooft coupling.
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.
New insights on non-perturbative Yang-Mills
Aguilar, Arlene C.
2010-11-12
In this talk we review some recent results on the infrared properties of the gluon and ghost propagators in pure Yang-Mills theories. These results are obtained from the corresponding Schwinger-Dyson equation formulated in a special truncation scheme, which preserves gauge invariance. The presence of massless poles in the three gluon vertex triggers the generation of a dynamical gluon mass (Schwinger mechanism in d = 4), which gives rise to an infrared finite gluon propagator and ghost dressing function. As a byproduct of this analysis we calculate the Kugo-Ojima function, required for the definition of the non-perturbative QCD effective charge within the pinch technique framework. We show that the numerical solutions of these non-perturbative equations are in very good agreement with the results of SU(3) lattice simulations.
Polyakov loop and gluon quasiparticles in Yang-Mills thermodynamics
NASA Astrophysics Data System (ADS)
Ruggieri, M.; Alba, P.; Castorina, P.; Plumari, S.; Ratti, C.; Greco, V.
2012-09-01
We study the interpretation of lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to transverse gluon quasiparticles by means of a gaslike effective potential. This study is useful to identify the effective degrees of freedom propagating in the gluon medium above the critical temperature. A main general finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop dynamics; hence, the thermodynamics can be described without the need for diverging or exponentially increasing quasiparticle masses as T→Tc, at variance respect to standard quasiparticle models.
NASA Astrophysics Data System (ADS)
Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto
2015-12-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g GF 2 ˜ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-07-01
The tree-level S-matrix of Einstein's theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1) M . The second operation turns gravitons into gluons and we call it "squeezing". This gives rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills. Dimensionally reducing Yang-Mills we find the S-matrix of a special Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of a YMS theory with an additional cubic scalar vertex. A corollary of the YMS formula gives one for a single massless scalar with a ϕ 4 interaction. Starting again from Einstein's theory but in d + d dimensions we introduce a "generalized dimensional reduction" that produces the Born-Infeld theory or a special Galileon theory in d dimensions depending on how it is applied. An extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI) theory. By applying the same operation to Yang-Mills we obtain the U( N ) non-linear sigma model (NLSM). Finally, we show how the Kawai-Lewellen-Tye relations naturally follow from our formulation and provide additional connections among these theories. One such relation constructs DBI from YMS and NLSM.
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...
A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model
Shimasaki, Shinji
2008-11-23
We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored.
The Polarization Tensor of the Massless Mode in Yang-Mills Thermodynamics
Schwarz, Markus
2011-09-22
We discuss the constraints on energy-momentum transfers in local vertices in the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics. Subsequently, we apply these constraints to the computation of the polarization tensor of the massless mode on the one-loop level. The resulting gap equation for the sought-after screening function is solved numerically. We discuss and interpret our results.
The Infrared Behaviour of the Pure Yang-Mills Green Functions
NASA Astrophysics Data System (ADS)
Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.; Micheli, J.; Pène, O.; Rodríguez-Quintero, J.
2012-10-01
We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from " quenched" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.
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.
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.
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.
Generalized Yang-Mills actions from Dirac operator determinants
NASA Astrophysics Data System (ADS)
Langmann, Edwin
2001-11-01
We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.
NASA Astrophysics Data System (ADS)
Isobe, Takeshi; Marini, Antonella
2012-06-01
In this paper, we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the ɛ-Dirichlet problem obtained as a variational problem for the SU(2)ɛ-Yang-Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem for the SU(2)-Yang-Mills functional with small boundary data. In the first paper of this series this non-compact variational problem is transformed into the finite-dimensional problem of finding the critical points of the function J_{ɛ }({q}), which is essentially the Yang-Mills functional evaluated on the approximate solutions, constructed via a gluing technique. In the present paper, we establish a Morse theory for J_{ɛ }({q}), by means of Ljusternik-Schnirelmann theory, thus complete the proofs of Theorems 1-3 given by Isobe and Marini ["Small coupling limit and multiple solutions to the Dirichlet Problem for Yang-Mills connections in 4 dimensions - Part I," J. Math. Phys. 53, 063706 (2012)], 10.1063/1.4728211.
Yang-Mills radiation in ultrarelativistic nuclear collisions
NASA Astrophysics Data System (ADS)
Gyulassy, M.; McLerran, L.
1997-10-01
The classical Yang-Mills radiation computed in the McLerran-Venugopalan model is shown to be equivalent to the gluon bremsstrahlung distribution to lowest (g6) order in pQCD. The classical distribution is also shown to match smoothly onto the conventional pQCD minijet distribution at a scale k2⊥~χ, characteristic of the initial parton transverse density of the system. The atomic number and energy dependence of χ is computed from available structure function information. The limits of applicability of the classical Yang-Mills description of nuclear collisions at RHIC and LHC energies are discussed.
Some remarks on representations of Yang-Mills algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2015-01-01
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra 𝔶𝔪(n) on n generators, for n ≥ 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of 𝔶𝔪(n) for n ≥ 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ≥ 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from 𝔶𝔪(3) to 𝔰𝔩(2, k) has in fact solvable image.
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.
Three-dimensional super Yang-Mills with compressible quark matter
NASA Astrophysics Data System (ADS)
Faedo, Antón F.; Kundu, Arnab; Mateos, David; Pantelidou, Christiana; Tarrío, Javier
2016-03-01
We construct the gravity dual of three-dimensional, SU(N c) super Yang-Mills theory with N f flavors of dynamical quarks in the presence of a non-zero quark density N q. The supergravity solutions include the backreaction of N c color D2-branes and N f flavor D6-branes with N q units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ = N c 2 N q/ λ 2 N f 4 , with λ = g YM 2 N c the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z = 5 and θ = 1, respectively. If ρ ≪ 1 then at intermediate energies there is also an approximate AdS4 region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass M q the physics depends non-trivially on ρ and M q N c /λ N f.
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.
Super Yang-Mills and θ-exact Seiberg-Witten map: absence of quadratic noncommutative IR divergences
NASA Astrophysics Data System (ADS)
Martin, Carmelo P.; Trampetic, Josip; You, Jiangyang
2016-05-01
We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N=1,2,4 super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.
Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops
Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.; /Moscow State U.
2005-05-27
We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.
NASA Astrophysics Data System (ADS)
Isobe, Takeshi; Marini, Antonella
2012-06-01
In this paper and its sequel (Part II), we analyze the space of solutions to the ɛ-Dirichlet problem for the Yang-Mills equations on the four-dimensional disk, for small values of the coupling constant ɛ. These are in 1-1 correspondence with solutions to the Dirichlet problem for Yang-Mills, for small boundary data ɛA0. We establish a Morse theory for this non-compact variational problem and prove the existence of multiple solutions, and, also, non minimal ones. Here, we describe the problem, state the main theorems and do the first part of the proof. This consists in making the problem finite dimensional, by seeking solutions approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. By introducing an auxiliary equation, we solve the problem orthogonally to the space of the approximate solutions.
The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary
NASA Astrophysics Data System (ADS)
Charalambous, Nelia; Gross, Leonard
2013-02-01
Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H 1. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.
Subleading terms in the collinear limit of Yang-Mills amplitudes
NASA Astrophysics Data System (ADS)
Stieberger, Stephan; Taylor, Tomasz R.
2015-11-01
For two massless particles i and j, the collinear limit is a special kinematic configuration in which the particles propagate with parallel four-momentum vectors, with the total momentum P distributed as pi = xP and pj = (1 - x) P, so that sij ≡(pi +pj) 2 =P2 = 0. In Yang-Mills theory, if i and j are among N gauge bosons participating in a scattering process, it is well known that the partial amplitudes associated to the (single trace) group factors with adjacent i and j are singular in the collinear limit and factorize at the leading order into (N - 1)-particle amplitudes times the universal, x-dependent Altarelli-Parisi factors. We give a precise definition of the collinear limit and show that at the tree level, the subleading, non-singular terms are related to the amplitudes with a single graviton inserted instead of two collinear gauge bosons. To that end, we argue that in one-graviton Einstein-Yang-Mills amplitudes, the graviton with momentum P can be replaced by a pair of collinear gauge bosons carrying arbitrary momentum fractions xP and (1 - x) P.
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.
Yang-Mills localization in warped space
Batell, Brian; Gherghetta, Tony
2007-01-15
We present a mechanism to localize zero mode non-Abelian gauge fields in a slice of AdS{sub 5}. As in the U(1) case, bulk and boundary mass terms allow for a massless mode with an exponential profile that can be localized anywhere in the bulk. However in the non-Abelian extension, the cubic and quartic zero-mode gauge couplings do not match, implying a loss of 4D gauge invariance. We show that the symmetry can be restored at the nonlinear level by considering brane-localized interactions, which are added in a gauge invariant way using boundary kinetic terms. Possible issues related to the scalar sector of the theory, such as strong coupling and ghosts, are also discussed. Our approach is then compared with other localization mechanisms motivated by dilaton gravity and deconstruction. Finally, we show how to localize the scalar component A{sub 5} zero mode anywhere in the bulk which could be relevant in gauge-Higgs unification models.
Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G 2-structure
NASA Astrophysics Data System (ADS)
Haupt, Alexander S.
2016-03-01
We study {g} -valued Yang-Mills fields on cylinders Zleft(G/Hright)={R}× G/H , where G/H is a compact seven-dimensional coset space with G 2-structure, {g} is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in {{R}}^n under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel G 2-structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.
Neumann domination for the Yang-Mills heat equation
NASA Astrophysics Data System (ADS)
Charalambous, Nelia; Gross, Leonard
2015-07-01
Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper, we improve on previous estimates by using a Neumann domination technique that allows us to get much better pointwise bounds on the magnetic field. As in the earlier work, we focus on Dirichlet, Neumann, and Marini boundary conditions. In addition, we show that the Wilson Loop functions, gauge invariantly regularized, converge as the parabolic time goes to infinity.
Extended 2D generalized dilaton gravity theories
NASA Astrophysics Data System (ADS)
de Mello, R. O.
2008-09-01
We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincaré algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincaré algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson Sigma models based on a nonlinear deformation of the extended Poincaré algebra.
Gluon scattering in N = 4 Super Yang-Mills at finite temperature
Ito, Katsushi; Iwasaki, Koh; Nastase, Horatiu
2008-11-23
We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N = 4 Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike 'Wilson loop' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric, thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a gauge theory observable that can be interpreted as the amplitude at strong coupling in both cut-off and generalized dimensional regularization.
Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex
Gover, A. R.; Hallowell, K.; Waldron, A.
2007-01-15
Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.
Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime
NASA Astrophysics Data System (ADS)
Gérard, C.; Wrochna, M.
2015-07-01
We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.
Color-kinematics duality for pure Yang-Mills and gravity at one and two loops
NASA Astrophysics Data System (ADS)
Bern, Zvi; Davies, Scott; Dennen, Tristan; Huang, Yu-tin; Nohle, Josh
2015-08-01
We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.
Hydrodynamics of the Polyakov line in SU(Nc) Yang-Mills
NASA Astrophysics Data System (ADS)
Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail
2016-02-01
We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite Nc for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of Nc, and are consistent with the string model results at Nc = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z (Nc) bubble using a piece-wise sound wave is suggested.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Catterall, Simon; Galvez, Richard; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
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.
Gravity duals for the Coulomb branch of marginally deformed Script N = 4 Yang-Mills
NASA Astrophysics Data System (ADS)
Hernández, Rafael; Sfetsos, Konstadinos; Zoakos, Dimitrios
2006-03-01
Supergravity backgrounds dual to a class of exactly marginal deformations of Script N = 4 supersymmetric Yang-Mills can be constructed through an SL(2,Bbb R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of Script N = 1 theories at strong 't Hooft coupling as marginal deformations of Script N = 4 Yang-Mills. For concreteness we concentrate to cases with an SO(4) × SO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrödinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.
Self-dual Yang-Mills fields in an Einstein universe
Pavlov, A. )
1992-12-01
Instanton solutions of Yang-Mills fields in flat Euclidean space have importance in studying the guage field vacuum. The authors find exact solutions of the self-consistent Einstein-Yang-Mills system of equations. These solutions are self-dual Yang-Mills fields in I[sup 1] [times] S[sup 3] space-time. The self-dual solutions have trivial topology and do not belong to instatons. The results of this study may help in understanding the vacuum structure of the fields under consideration. 4 refs.
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.
Kinetic energy for the nuclear Yang-Mills collective model
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2015-10-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM, has two hidden mathematical structures, one Lie group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new unexplored feature that shares the same mathematical origin as Yang-Mills, viz., a vector bundle with a non-abelian structure group and a connection. Using the de Rham Laplacian ▵ = * d * d from differential geometry for the kinetic energy extends significantly the physical scope of the GCM model. This Laplacian contains a ``magnetic'' term due to the coupling between base manifold rotational and fiber vorticity degrees of freedom. When the connection specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator. More generally, the connection yields a moment of inertia that is intermediate between the extremes of irrotational flow and rigid body motion.
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.
Towards a string bit formulation of Script N = 4 super Yang-Mills
NASA Astrophysics Data System (ADS)
Alday, Luis F.; David, Justin R.; Gava, Edi; Narain, Kumar S.
2006-04-01
We show that planar Script N = 4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.
Massive Yang-Mills for vector and axial-vector spectral functions at finite temperature
NASA Astrophysics Data System (ADS)
Hohler, Paul M.; Rapp, Ralf
2016-05-01
The hadronic mechanism which leads to chiral symmetry restoration is explored in the context of the ρπa1 system using Massive Yang-Mills, a hadronic effective theory which governs their microscopic interactions. In this approach, vector and axial-vector mesons are implemented as gauge bosons of a local chiral gauge group. We have previously shown that this model can describe the experimentally measured vector and axial-vector spectral functions in vacuum. Here, we carry the analysis to finite temperatures by evaluating medium effects in a pion gas and calculating thermal spectral functions. We find that the spectral peaks in both channels broaden along with a noticeable downward mass shift in the a1 spectral peak and negligible movement of the ρ peak. The approach toward spectral function degeneracy is accompanied by a reduction of chiral order parameters, i.e., the pion decay constant and scalar condensate. Our findings suggest a mechanism where the chiral mass splitting induced in vacuum is burned off. We explore this mechanism and identify future investigations which can further test it.
Chaotic dynamics of Yang-Mills field as source of particle couplings and masses
Goldfain, E.
1995-04-01
Dynamics of classical uniform Yang-Mills fields is explored from the viewpoint of universal route to chaos in nonlinear systems. The author shows how the path to nonintegrable behavior of the field is equivalent to the period doubling bifurcation of the logistic map. Universal scalings of the growth parameter yield the full set of Standard Model couplings. Hamiltonian formulation in action-angle variables leads to the physics of phase transitions in classical lattice models. The ground state phase diagram of the system with {open_quotes}antiferromagnetic{close_quotes} interaction is known to exhibit a devil`s staircase form. Linking the staircase attributes to the asymptotic freedom of the gauge coupling yields an universal mass equation. Critical exponent is found to depend on the number of field flavors. Further solving the model for various stability plateaus renders the spectrum of particle masses in the low energy framework. Agreement between theory and experimental results is confirmed for the photon/graviton pair, weak bosons, leptons and quarks. The approach offers an intriguing explanation of the dymanical origin of the physical mass and on the internal hierarchy of particle families.
Dynamics of Euclideanized Einstein-Yang-Mills systems with arbitrary gauge groups
Bertolami, O.; Picken, R.F. ); Maurao, J.M. ); Volobujev, I.P. )
1991-09-30
This paper describes the dynamics of euclideanized SO(4)-symmetric Einstein-Yang-Mills (EYM) systems with arbitrary compact gauge groups K. For the case of SO(n) and SU(n) gauge groups and simple embeddings of the isotropy group in K, the authors show that in the resulting dynamical system, the Friedmann equation decouples from the Yang-Mills equations. Furthermore, the latter can be reduced to a system of two second-order differential equations. This allows the authors to find a broad class of instanton (wormhole) solutions of the EYM equations. These solutions are not afflicted by the giant-wormhole catastrophe.
A Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
NASA Astrophysics Data System (ADS)
Navarro-Lérida, Francisco; Radu, Eugen; Tchrakian, D. H.
2014-10-01
We study spherically symmetric solutions of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions. The Chern-Simons densities are defined in terms of both Yang-Mills fields and a five-component isomultiplet Higgs. The SO(3) × SO(2) solutions are analyzed in a systematic way, by employing numerical methods. These finite energy configurations possess both electric and magnetic global charges, differing radically, however, from Julia-Zee dyons. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
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.
5D radiating black holes in Einstein-Yang-Mills-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Ghosh, S. G.
2011-10-01
We derive nonstatic spherically symmetric solutions of a null fluid, in five dimension (5D), to Einstein-Yang-Mills (EYM) equations with the coupling of Gauss-Bonnet (GB) combination of quadratic curvature terms, namely, 5D EYMGB radiating black hole solution. It is shown that, in the limit, we can recover known radiating black hole solutions. The spherically symmetric known 5D static black hole solutions are also retrieved. The effect of the GB term and Yang-Mills (YM) gauge charge on the structure and location of horizons, of the 5D radiating black hole, is also discussed.
NASA Astrophysics Data System (ADS)
Challifour, John L.; Timko, Edward J.
2016-06-01
Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint.
Two-loop five-point all-plus helicity Yang-Mills amplitude
NASA Astrophysics Data System (ADS)
Dunbar, David C.; Perkins, Warren B.
2016-04-01
We recompute the recently derived two-loop five-point all-plus Yang-Mills amplitude using unitarity and recursion. Recursion requires augmented recursion to determine the subleading pole. Using these methods, the simplicity of this amplitude is understood.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.; Melnikov, V. N.
2014-01-01
In the framework of 10-dimensional "Friedmann-Calabi-Yau" cosmology of superstring origin we show that the time variation of either Newton's gravitational constant or Yang-Mills one is unavoidable in the present epoch.
Nonperturbative construction of massive Yang-Mills fields without the Higgs field
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2013-01-01
In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written by using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation, and color rotation.
Wang, L. C.
1980-01-01
Bäecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure.
Number of gauge singlets in supersymmetric Yang-Mills quantum mechanics
Trzetrzelewski, Maciej
2007-10-15
We calculate generating functions for a number of U(N) (SU(N)) singlets in Fock space in several space dimensions. The motivation to find the explicit form of the functions is from the numerical approach applied to supersymmetric Yang-Mills quantum mechanics, based on Fock space. Incidentally the functions give many important insights into the quantum mechanical models based on U(N)(SU(N)) gauge group.
Critical Wavelike Behaviour in Stringy Gravity with Yang Mills Source and Cosmological Constant
Slagter, Reinoud J.; Masselink, Derk
2006-11-03
We investigate numerically the behaviour of the self-gravitating coupled Einstein-Yang-Mills system on an axially symmetric five dimensional space time, with and without the Gauss-Bonnet term. We observe that the critical behaviour at the threshold of black hole formation is present in the 5-dimensional model and depends critically on the value of the cosmological constant and the Gauss-Bonnet coupling.
Reductions of self-dual Yang-Mills fields and classical systems
NASA Astrophysics Data System (ADS)
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
1990-08-01
One-dimensional reductions of the self-dual Yang-Mills equations yield various classical systems depending on the choice of the Lie algebra associated with the self-dual fields. Included are the Euler-Arnold equations for rigid bodies in n dimensions, the Kovalevskaya top, and a generalization of the Nahm equation which is related to a classical third-order differential equation possessing a movable natural boundary in the complex plane.
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.
Structure constants of β deformed super Yang-Mills
NASA Astrophysics Data System (ADS)
David, Justin R.; Sadhukhan, Abhishake
2013-10-01
We study the structure constants of the beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then studythe structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS 5 × S 5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.
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.
A New Reduction of the Self-Dual Yang-Mills Equations and its Applications
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Wang, Yan
2016-07-01
Through imposing on space-time symmetries, a new reduction of the self-dual Yang-Mills equations is obtained for which a Lax pair is established. By a proper exponent transformation, we transform the Lax pair to get a new Lax pair whose compatibility condition gives rise to a set of partial differential equations (PDEs). We solve such PDEs by taking different Lax matrices; we develop a new modified Burgers equation, a generalised type of Kadomtsev-Petviasgvili equation, and the Davey-Stewartson equation, which also generalise some results given by Ablowitz, Chakravarty, Kent, and Newman.
Attractor Solution in Coupled Yang-Mills Field Dark Energy Models
NASA Astrophysics Data System (ADS)
Zhao, Wen
We investigate the attractor solution in the coupled Yang-Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation of state of dark energy must evolve from wy > 0 to wy ≤ -1, which is slightly suggested by the observation. At the same time, the total equation of state in the attractor solution is wtot = -1, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.
One-loop amplitudes in Script N = 4 super Yang-Mills and anomalous dual conformal symmetry
NASA Astrophysics Data System (ADS)
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele
2009-08-01
We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard and one-mass supercoefficients which appears in the supersymmetric on-shell recursion relations and equals the corresponding tree-level superamplitude. We discuss further novel relations among supercoefficients imposed by the remaining non-anomalous part of the symmetry. In particular, we find that all one-loop supercoefficients, except the four-mass box coefficients, can be expressed as linear combinations of three-mass box coefficients and a particular symmetric combination of two-mass hard coefficients. We check that our equations are explicitly satisfied in the case of one-loop n-point MHV and NMHV amplitudes. As a bonus, we prove the covariance of the NMHV superamplitudes at an arbitrary number of points, extending previous results at n <= 9.
The 2d MIT: The Pseudogap and Fermi Liquid Theory
NASA Astrophysics Data System (ADS)
Castner, T. G.
2005-06-01
Fermi liquid theory for the 2d metal-insulator transition is extended to include the correlation gap in the density-of-states. The results are consistent with the scaling form g=gce[on(To/T)] at T larger than a characteristic T* ∝ xTc (Tc=Ec= mobility edge). The two-component model n1+nloc=n=nc(1+x) for n>nc is required and the theory explains the T-dependence of the data of Hanein et al. for p-type GaAs.
The unitary conformal field theory behind 2D Asymptotic Safety
NASA Astrophysics Data System (ADS)
Nink, Andreas; Reuter, Martin
2016-02-01
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.
Steady 2D Detonations and the DSD Theory
NASA Astrophysics Data System (ADS)
Lubyatinsky, S. N.; Loboiko, B. G.; Filin, V. P.; Kostitsin, O. V.; Smirnov, E. B.
2006-07-01
In the framework of the simplest DSD theory we obtained ODEs describing steady 2D detonation front shapes for slab, cylinder, and rib geometries. It was found that one solution (a steady detonation front shape) corresponds to several combinations of the confinement material and the defining charge dimension (slab thickness, cylinder radius, or inner rib radius). Comparing experimental data for these combinations and analyzing the shape difference at the edge provide information on the D(κ) relation at low D. The analysis of the data on IHE ribs detonation indicates that as D decreases total curvature κ tends to a limit of about 0.1 mm-1, i.e., double the reciprocal critical diameter. This correction makes the DSD theory consistent with the experimental critical diameter.
NASA Astrophysics Data System (ADS)
Yablon, Jay R.
2013-10-01
Evidence is summarized from four recent papers that baryons including protons and neutrons are magnetic monopoles of non-commuting Yang-Mills gauge theories: 1) Protons and neutrons are ``resonant cavities'' with binding energies determined strictly by the masses of the quarks they contain. This is proven true at parts-per million accuracy for each of the 2H, 3H,3He, 4He binding energies and the neutron minus proton mass difference. 2) Respectively, each free proton and neutron contains 7.64 MeV and 9.81 MeV of mass/energy used to confine its quarks. When these nucleons bind, some, never all, of this energy is released and the mass deficit goes into binding. The balance continues to confine quarks. 56Fe releases 99.8429% of this energy for binding, more than any other nuclide. 3) Once we consider the Fermi vev one also finds an entirely theoretical explanation of proton and neutron masses, which also connects within experimental errors to the CKM quark mixing angles. 4) A related GUT explains fermion generation replication based on generator loss during symmetry breaking, and answers Rabi's question ``who ordered this?'' 5) Nuclear physics is governed by combining Maxwell's two classical equations into one equation using non-commuting gauge fields in view of Dirac theory and Fermi-Dirac-Pauli Exclusion. 6) Atoms themselves are core magnetic charges (nucleons) paired with orbital electric charges (electrons and elusive neutrinos), with the periodic table itself revealing an electric/magnetic symmetry of Maxwell's equations often pondered but heretofore unrecognized for a century and a half.
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.
A new phase for the anisotropic N=4 super Yang-Mills plasma
NASA Astrophysics Data System (ADS)
Banks, Elliot; Gauntlett, Jerome P.
2015-09-01
Black hole solutions of type IIB supergravity have been previously constructed that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. The zero temperature limit of these black holes approach a Lifshitz-like scaling solution in the infrared. We show that these black holes become unstable at low temperature and we construct a new class of black hole solutions which are thermodynamically preferred. The phase transition is third order and incorporates a spontaneous breaking of the SO(6) global symmetry down to SO(4) × SO(2). The critical exponents for the phase transition are given by ( α, β, γ, δ) = (-1, 1, 1, 2) which differ from the standard mean-field exponents usually seen in holography. At low temperatures the black holes approach a novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation. We show that the new ground states are thermal insulators in the direction of the anisotropy.
Pion in the Holographic Model with 5D Yang-Mills Fields
Grigoryan, Hovhannes; Radyushkin, Anatoly
2008-12-01
We study pion in the holographic model of Hirn and Sanz which contains two Yang-Mills fields defined in the background of the sliced AdS space. The infrared boundary conditions imposed on these fields generate the spontaneous breaking of the chiral symmetry down to its vector subgroup. Within the framework of this model, we get an analytic expression for the pion form factor and a compact result for its radius. We also extend the holographic model to include Chern-Simons term which is required to reproduce the appropriate axial anomaly of QCD. As a result, we calculate the anomalous form factor of the pion and predict its Q^2-slope for the kinematics when one of the photons is almost on-shell. We also observe that the anomalous form factor with one real and one virtual photon is given by the same analytic expression as the electromagnetic form factor of a charged pion.
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.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
2015-10-01
We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
Kinematic numerators and a double-copy formula for N=4 super-Yang-Mills residues
NASA Astrophysics Data System (ADS)
Litsey, Sean; Stankowicz, James
2014-07-01
Recent work by Cachazo et al.arXiv:1309.0885 shows that connected prescription residues obey the global identities of N=4 super-Yang-Mills amplitudes. In particular, they obey the Bern-Carrasco-Johansson (BCJ) amplitude identities. Here we offer a new way of interpreting this result via objects that we call residue numerators. These objects behave like the kinematic numerators introduced by BCJ except that they are associated with individual residues. In particular, these new objects satisfy a double-copy formula relating them to the residues appearing in recently discovered analogs of the connected prescription integrals for N=8 supergravity. Along the way, we show that the BCJ amplitude identities are equivalent to the consistency condition that allows kinematic numerators to be expressed as amplitudes using a generalized inverse.
Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions
Radu, Eugen; Tchrakian, D. H.; Yang Yisong
2008-02-15
We present several different classes of self-dual Yang-Mills instantons in all even d-dimensional backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti-de Sitter) backgrounds and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.
Exact solutions of (n+1)-dimensional Yang-Mills equations in curved space-time
Sanchez-Monroy, J.A.; Quimbay, C.J.
2012-09-15
In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time, for the cases n=1,2,3. As an application of the results obtained for the case n=3, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case n=2 is a description of the (2+1) electrodynamics in the presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case n=1 is invariant under a parity transformation and has the form of a linear confining solution. - Highlights: Black-Right-Pointing-Pointer We study exact static confining solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time. Black-Right-Pointing-Pointer The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background. Black-Right-Pointing-Pointer A expression for the confinement potential in low dimensionality is found.
Steady 2d Detonations and the DSD Theory
NASA Astrophysics Data System (ADS)
Lubyatinsky, Sergey N.
2005-07-01
The simplest Detonation Shock Dynamics (DSD) theory assumes that the detonation normal velocity D is determined by the total front curvature k and that the edge angle, the angle between the normal to the front and the explosive edge, has a unique value for each explosive and confinement material combination. This model has been used to derive the ordinary differential equations describing steady 2D detonation front shapes in slab, cylinder and rib geometries. It was found that one solution (a steady detonation front shape) corresponds to several combinations of the confinement material and the defining charge dimension (slab thickness, cylinder radius, or inner rib radius). Comparing experimental data for these combinations and analyzing the shape difference at the edge provide valuable information on the D(k) relation at low D corresponding to forced detonation regimes. The analysis of the experimental data on IHE ribs detonation indicates that as D decreases k tends to a limit of about 0.05 1/mm, i.e., of the order of reciprocal critical diameter. This revises the present view of the D(k) relation making the DSD theory consistent with the experimentally observed critical diameter.
NASA Astrophysics Data System (ADS)
Stoecker, Horst; Zhou, Kai; Schramm, Stefan; Senzel, Florian; Greiner, Carsten; Beitel, Maxim; Gallmeister, Kai; Gorenstein, Mark; Mishustin, Igor; Vasak, David; Steinheimer, Jan; Struckmeier, Juergen; Vovchenko, Volodymyr; Satarov, Leonid; Xu, Zhe; Zhuang, Pengfei; Csernai, Laszlo P.; Sinha, Bikash; Raha, Sibaji; Sándor Biró, Tamás; Panero, Marco
2016-08-01
The early stage of a high multiplicity pp, pA and AA collisions is represented by a nearly quarkless, hot, deconfined pure gluon plasma. According to pure Yang-Mills lattice gauge theory, this hot pure glue matter undergoes, at a high temperature, {T}c=270 {{MeV}}, a first-order phase transition into a confined Hagedorn glueball fluid. This new scenario should be characterized by a suppression of high p T photons and dileptons, baryon suppression and enhanced strange meson production. We propose to observe this newly predicted class of events at the Large Hadron Collider and the Relativistic Heavy-Ion Collider.
Daniel Heineman Prize: QCD, strings and black holes: A duality between gravity and field theory
NASA Astrophysics Data System (ADS)
Maldacena, Juan
2007-04-01
We discuss Yang Mills theory with a large number of colors. In this limit it becomes a theory of strings. We describe the string theory associated to the most supersymmetric version of Yang Mills theory. These strings live in a ten dimensional curved space. Thus supersymmetric Yang Mills theory is related to the ordinary ten dimensional superstring theory which describes quantum gravity. We will review some results in this area and discuss some recent developments. We will also discuss the implications for black hole entropy and the black hole information puzzle.
Density functional theory for polymeric systems in 2D
NASA Astrophysics Data System (ADS)
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-01
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.
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. PMID:27115343
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.
Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
NASA Astrophysics Data System (ADS)
Mafra, Carlos R.; Schlotterer, Oliver
2015-10-01
Supersymmetric integrands for the two-loop five-point amplitudes in tendimensional super Yang-Mills and type II supergravity are proposed. The kinematic numerators are manifestly local and satisfy the duality between color and kinematics described by Bern, Carrasco and Johansson. Our results are expected to reproduce the integrated two-loop amplitudes in dimensions D < 7. The UV divergence in the critical dimension D = 7 matches the low-energy limit of the corresponding superstring amplitudes and is written in terms of SYM tree amplitudes.
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.
Infrared analysis of propagators and vertices of Yang-Mills theory in Landau and Coulomb gauge
Schleifenbaum, W.; Leder, M.; Reinhardt, H.
2006-06-15
The infrared behavior of gluon and ghost propagators, ghost-gluon vertex, and three-gluon vertex is investigated for both the covariant Landau and the noncovariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behavior of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.
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.
Pomeron Eigenvalue at Three Loops in N=4 Supersymmetric Yang-Mills Theory.
Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
2015-12-18
We obtain an analytical expression for the next-to-next-to-leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar N=4 SYM using quantum spectral curve (QSC) integrability-based method. The result is verified with more than 60-digit precision using the numerical method developed by us in a previous paper [N. Gromov, F. Levkovich-Maslyuk, and G. Sizov, arXiv:1504.06640]. As a by-product, we developed a general analytic method of solving the QSC perturbatively. PMID:26722913
On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields
Alkofer, Reinhard; Maas, Axel; Macher, Veronika; Fister, Leonard
2011-05-23
Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhibiting interesting cancellations purely due to colour algebra.
Lattice evidence for the family of decoupling solutions of Landau gauge Yang-Mills theory
NASA Astrophysics Data System (ADS)
Sternbeck, André; Müller-Preussker, Michael
2013-10-01
We show that the low-momentum behavior of the lattice Landau-gauge gluon and ghost propagators is sensitive to the lowest non-trivial eigenvalue (λ1) of the Faddeev-Popov operator. If the gauge fixing favors Gribov copies with small λ1 the ghost dressing function rises more rapidly towards zero momentum than on copies with large λ1. This effect is seen for momenta below 1 GeV, and interestingly also for the gluon propagator at momenta below 0.2 GeV: For large λ1 the gluon propagator levels out to a lower value at zero momentum than for small λ1. For momenta above 1 GeV no dependence on Gribov copies is seen. Although our data is only for a single lattice size and spacing, a comparison to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski (2009) [22] yields already a good qualitative agreement.
NASA Astrophysics Data System (ADS)
Killingback, T. P.
1991-05-01
We define a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group. This theory is defined in terms of intersection theory on the moduli space of flat connections on a two-dimensional surface and corresponds physically to a two-dimensional reduction and truncation of four-dimensional topological Yang-Mills theory. Two-dimensional topological Yang-Mills theory defines a topological matter system and may be naturally coupled to two-dimensional topological gravity. This topological Yang-Mills theory is also closely related to Chern-Simons gauge theory in 2 + 1 dimensions. We also discuss a relation between SL (2, R) Chern-Simons theory and two-dimensional topological gravity.
Monochromatic Wannier Functions in the Theory of 2D Photonic Crystals and Photonic Crystal Fibers
Mazhirina, Yu. A.; Melnikov, L. A.
2011-10-03
The use of the monochromatic Wannier functions which have the temporal dependence as (exp(-i{omega}t)) in the theory of 2D photonic crystals and photonic crystal fibers is proposed. Corresponding equations and formulae are derived and discussed.
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.
Lorenz-Mie theory for 2D scattering and resonance calculations
NASA Astrophysics Data System (ADS)
Gagnon, Denis; Dubé, Louis J.
2015-10-01
This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell’s equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.
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. PMID:19519096
Sehgal, Akansha Ashvani; Pelupessy, Philippe; Rolando, Christian; Bodenhausen, Geoffrey
2016-04-01
Two-dimensional (2D) Fourier transform ion cyclotron resonance (FT-ICR) offers an approach to mass spectrometry (MS) that pursuits similar objectives as MS/MS experiments. While the latter must focus on one ion species at a time, 2D FT ICR can examine all possible correlations due to ion fragmentation in a single experiment: correlations between precursors, charged and neutral fragments. We revisited the original 2D FT-ICR experiment that has hitherto fallen short of stimulating significant analytical applications, probably because it is technically demanding. These shortcomings can now be overcome by improved FT-ICR instrumentation and computer hard- and software. We seek to achieve a better understanding of the intricacies of the behavior of ions during a basic two-dimensional ICR sequence comprising three simple monochromatic pulses. Through simulations based on Lorentzian equations, we have mapped the ion trajectories for different pulse durations and phases. PMID:26974979
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.
Wilson loops in supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Pestun, Vasily
This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.
NASA Astrophysics Data System (ADS)
Navarro-Lérida, Francisco; Tchrakian, D. H.
2015-05-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3+1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.
Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju
2013-01-01
Anisotropic flow coefficients v(1)-v(5) in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated v(n) data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v(2), v(3) and v(4) measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined. PMID:23383781
NASA Astrophysics Data System (ADS)
Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju
2013-01-01
Anisotropic flow coefficients v1-v5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated vn data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v2, v3 and v4 measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.
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.
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
Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta
NASA Astrophysics Data System (ADS)
Kumar, R.; Gupta, S.; Malik, R. P.
2016-06-01
We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
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.
Perturbative gauge theory at null infinity
NASA Astrophysics Data System (ADS)
Adamo, Tim; Casali, Eduardo
2015-06-01
We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.
Possibility of gravitational quantization under the teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Ming, Kian; Triyanta, Kosasih, J. S.
2016-03-01
Teleparallel gravity (TG) or tele-equivalent general relativity (TEGR) is an alternative gauge theory for gravity. In TG tetrad fields are defined to express gravitational fields and act like gauge potentials in standard gauge theory. The lagrangians for the gravitational field in TG and for the Yang-Mills field in standard gauge theory differ due to different indices that stick on the components of the corresponding fields: two external indices for tetrad field and internal and external indices for the Yang-Mills field. Different types of indices lead to different possible contractions and thus lead to different expression of the lagrangian for the Yang Mills field and for the tetrad field. As TG is a gauge theory it is then natural to quantize gravity in TG by applying the same procedure of quantization as in the standard gauge theory. Here we will discuss on the possibility to quantize gravity, canonically and functionally, under the framework of TG theory.
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.
Probability distribution of the index in gauge theory on 2d non-commutative geometry
NASA Astrophysics Data System (ADS)
Aoki, Hajime; Nishimura, Jun; Susaki, Yoshiaki
2007-10-01
We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index ν of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of ν by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under ν mapsto -ν, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.
Study on 2D random medium inversion algorithm based on Fuzzy C-means Clustering theory
NASA Astrophysics Data System (ADS)
Xu, Z.; Zhu, P.; Gu, Y.; Yang, X.; Jiang, J.
2015-12-01
Abstract: In seismic exploration for metal deposits, the traditional seismic inversion method based on layered homogeneous medium theory seems difficult to inverse small scale inhomogeneity and spatial variation of the actual medium. The reason is that physical properties of actual medium are more likely random distribution rather than layered. Thus, it is necessary to investigate a random medium inversion algorithm. The velocity of 2D random medium can be described as a function of five parameters: the background velocity (V0), the standard deviation of velocity (σ), the horizontal and vertical autocorrelation lengths (A and B), and the autocorrelation angle (θ). In this study, we propose an inversion algorithm for random medium based on the Fuzzy C-means Clustering (FCM) theory, whose basic idea is that FCM is used to control the inversion process to move forward to the direction we desired by clustering the estimated parameters into groups. Our method can be divided into three steps: firstly, the three parameters (A, B, θ) are estimated from 2D post-stack seismic data using the non-stationary random medium parameter estimation method, and then the estimated parameters are clustered to different groups according to FCM; secondly, the initial random medium model is constructed with clustered groups and the rest two parameters (V0 and σ) obtained from the well logging data; at last, inversion of the random medium are conducted to obtain velocity, impedance and random medium parameters using the Conjugate Gradient Method. The inversion experiments of synthetic seismic data show that the velocity models inverted by our algorithm are close to the real velocity distribution and the boundary of different media can be distinguished clearly.Key words: random medium, inversion, FCM, parameter estimation
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).
Ward identities and renormalization of general gauge theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2004-02-01
We introduce the concept of general gauge theory which includes Yang-Mills models. We use the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields. For the Yang-Mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid. The investigation of higher orders of the perturbation theory is still an open problem.
Spinor helicity structures in higher spin theories
NASA Astrophysics Data System (ADS)
Ananth, Sudarshan
2012-11-01
It is shown that the coefficient of the cubic interaction vertex, in higher spin Lagrangians, has a very simple form when written in terms of spinor helicity products. The result for a higher-spin field, of spin λ, is equal to the corresponding Yang-Mills coefficient raised to the power λ. Among other things, this suggests perturbative ties, similar to the KLT relations, between higher spin theories and pure Yang-Mills. This result is obtained in four-dimensional flat spacetime.
New identities among gauge theory amplitudes
NASA Astrophysics Data System (ADS)
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
2010-08-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
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.
Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
NASA Astrophysics Data System (ADS)
Bern, Z.; Carrasco, J. J. M.; Dixon, L. J.; Johansson, H.; Roiban, R.
2012-05-01
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/Nc2 single-trace divergence in N=4 super-Yang-Mills theory.
NASA Astrophysics Data System (ADS)
Hsu, Jong-Ping
Within Yang-Mills gravity with translation group T(4) in flat space-time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations, which are shown to be consistent with experiments. The radiation power turns out to be the same as that in Einstein's gravity to the second-order approximation. We also discuss an interesting physical reason for the accelerated cosmic expansion based on the long-range Lee-Yang force of Ub(1) gauge field associated with the established conservation law of baryon number. We show that the Lee-Yang force can be related to a linear potential ∝ r, provided the gauge field satisfies a fourth-order differential equation in flat space-time. Furthermore, we consider an experimental test of the Lee-Yang force related to the accelerated cosmic expansion. The necessity of generalizing Lorentz transformations for accelerated frames of reference and accelerated Wu-Doppler effects are briefly discussed.
Differential Sensitivity Theory applied to the MESA2D code for multi-material problems
Henninger, R.J.; Maudlin, P.J.; Harstad, E.N.
1996-05-01
The technique called Differential Sensitivity Theory (DST) is extended to the multi-component system of equations solved by the MESA2D hydrocode. DST uses adjoint techniques to determine exact sensitivity derivatives, i.e., if R is a calculation result of interest (response R) and {alpha}{sub i} is a calculation input (parameter {alpha}{sub i}), then {partial_derivative}R/{partial_derivative}{alpha}{sub i} is defined as the sensitivity. The advantage of using DST is that for an n-parameter problem {ital all} n sensitivities can be obtained by integrating the solutions from only {ital two} calculations, a MESA calculation and its corresponding adjoint calculation using an Adjoint Continuum Mechanics (ACM) code. Previous papers have described application of the technique to one-dimensional, single-material problems. This work presents the derivation and solution of the additional adjoint equations for the purpose of computing sensitivities for two-dimensional, multi-component problems. As an example, results for a multi-material flyer plate impact problem featuring an oblique impact are given. {copyright} {ital 1996 American Institute of Physics.}
Differential Sensitivity Theory applied to the MESA2D code for multi-material problems
NASA Astrophysics Data System (ADS)
Henninger, R. J.; Maudlin, P. J.; Harstad, E. N.
1996-05-01
The technique called Differential Sensitivity Theory (DST) is extended to the multi-component system of equations solved by the MESA2D hydrocode. DST uses adjoint techniques to determine exact sensitivity derivatives, i.e., if R is a calculation result of interest (response R) and αi is a calculation input (parameter αi), then ∂R/∂αi is defined as the sensitivity. The advantage of using DST is that for an n-parameter problem all n sensitivities can be obtained by integrating the solutions from only two calculations, a MESA calculation and its corresponding adjoint calculation using an Adjoint Continuum Mechanics (ACM) code. Previous papers have described application of the technique to one-dimensional, single-material problems. This work presents the derivation and solution of the additional adjoint equations for the purpose of computing sensitivities for two-dimensional, multi-component problems. As an example, results for a multi-material flyer plate impact problem featuring an oblique impact are given.
Differential sensitivity theory applied to the MESA2D code for multi-material problems
Henninger, R.J.; Maudlin, P.J.; Harstad, E.N.
1995-09-01
The technique called Differential Sensitivity Theory (DST) is extended to the multi-component system of equations solved by the MESA2D hydrocode. DST uses adjoint techniques to determine exact sensitivity derivatives, i.e., if R is a calculation result of interest (response R) and {alpha}{sub i} is a calculation input (parameter {alpha}{sub i}), then {partial_derivative}R/{partial_derivative}{alpha}{sub i} is defined as the sensitivity. The advantage of using DST is that for an n-parameter problem all n sensitivities can be obtained by integrating the solutions from only two calculations, a MESA calculation and its corresponding adjoint calculation using an Adjoint Continuum Mechanics (ACM) code. Previous papers have described application of the technique to one-dimensional, single-material problems. This work presents the derivation and solution of the additional adjoint equations for the purpose of computing sensitivities for two-dimensional, multi-component problems. As an example, results for a multi-material flyer plate impact problem featuring an oblique impact are given.
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.
Probing non-perturbative effects in M-theory on orientifolds
NASA Astrophysics Data System (ADS)
Okuyama, Kazumi
2016-01-01
Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S 3 partition functions of dual field theories. We consider the S 3 partition functions of N=4 Yang-Mills theory with O( n) gauge symmetry coupled to one (anti)symmetric and N f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U( n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
NASA Astrophysics Data System (ADS)
Pestun, Vasily
2012-07-01
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the {N=4} supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure {N=2} and the {N=2^*} supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional {N=2} superconformal gauge theory is treated similarly.
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
Comparison of the 1D flux theory with a 2D hydrodynamic secondary settling tank model.
Ekama, G A; Marais, P
2004-01-01
The applicability of the 1D idealized flux theory (1DFT) for design of secondary settling tanks (SSTs) is evaluated by comparing its predicted maximum surface overflow (SOR) and solids loading (SLR) rates with that calculated from the 2D hydrodynamic model SettlerCAD using as a basis 35 full scale SST stress tests conducted on different SSTs with diameters from 30 to 45m and 2.25 to 4.1 m side water depth, with and without Stamford baffles. From the simulations, a relatively consistent pattern appeared, i.e. that the 1DFT can be used for design but its predicted maximum SLR needs to be reduced by an appropriate flux rating, the magnitude of which depends mainly on SST depth and hydraulic loading rate (HLR). Simulations of the sloping bottom shallow (1.5-2.5 m SWD) Dutch SSTs tested by STOWa and the Watts et al. SST, all with doubled SWDs, and the Darvill new (4.1 m) and old (2.5 m) SSTs with interchanged depths, were run to confirm the sensitivity of the flux rating to depth and HLR. Simulations with and without a Stamford baffle were also done. While the design of the internal features of the SST, such as baffling, have a marked influence on the effluent SS concentration for underloaded SSTs, these features appeared to have only a small influence on the flux rating, i.e. capacity, of the SST, In the meantime until more information is obtained, it would appear that from the simulations so far that the flux rating of 0.80 of the 1DFT maximum SLR recommended by Ekama and Marais remains a reasonable value to apply in the design of full scale SSTs--for deep SSTs (4 m SWD) the flux rating could be increased to 0.85 and for shallow SSTs (2.5 m SWD) decreased to 0.75. It is recommended that (i) while the apparent interrelationship between SST flux rating and depth suggests some optimization of the volume of the SST, that this be avoided and that (ii) the depth of the SST be designed independently of the surface area as is usually the practice and once selected, the
NASA Astrophysics Data System (ADS)
Yogurtcu, Osman N.; Johnson, Margaret E.
2015-08-01
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
The complete KLT-map between gravity and gauge theories
NASA Astrophysics Data System (ADS)
Damgaard, Poul H.; Huang, Rijun; Søndergaard, Thomas; Zhang, Yang
2012-08-01
We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
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.
2010-01-01
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. PMID:17441250
A one-loop test for construction of 4D N = 4 SYM from 2D SYM via fuzzy-sphere geometry
NASA Astrophysics Data System (ADS)
Matsuura, So; Sugino, Fumihiko
2016-04-01
As a perturbative check of the construction of 4D N=4 supersymmetric Yang-Mills theory (SYM) from mass-deformed N=(8,8) SYM on the 2D lattice, the one-loop effective action for scalar kinetic terms is computed in N=4 U(k) SYM on R^2 × (fuzzy S^2), which is obtained by expanding 2D N=(8,8) U(N) SYM with mass deformation around its fuzzy-sphere classical solution. The radius of the fuzzy sphere is proportional to the inverse of the mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal plane. It is straightforward at the classical level to obtain the ordinary N=4 SYM on R^4 in the limits, while it is nontrivial at the quantum level. The one-loop effective action for the SU(k) sector of the gauge group U(k) coincides with that of the ordinary 4D N=4 SYM in the above limits. Although a "noncommutative anomaly" appears in the overall U(1) sector of the U(k) gauge group, this can be expected to be a gauge artifact not affecting gauge-invariant observables.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
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 review on principles, theory and practices of 2D-QSAR.
Roy, Kunal; Das, Rudra Narayan
2014-01-01
The central axiom of science purports the explanation of every natural phenomenon using all possible logics coming from pure as well as mixed scientific background. The quantitative structure-activity relationship (QSAR) analysis is a study correlating the behavioral manifestation of compounds with their structures employing the interdisciplinary knowledge of chemistry, mathematics, biology as well as physics. Several studies have attempted to mathematically correlate the chemistry and property (physicochemical/ biological/toxicological) of molecules using various computationally or experimentally derived quantitative parameters termed as descriptors. The dimensionality of the descriptors depends on the type of algorithm employed and defines the nature of QSAR analysis. The most interesting feature of predictive QSAR models is that the behavior of any new or even hypothesized molecule can be predicted by the use of the mathematical equations. The phrase "2D-QSAR" signifies development of QSAR models using 2D-descriptors. Such predictor variables are the most widely practised ones because of their simple and direct mathematical algorithmic nature involving no time consuming energy computations and having reproducible operability. 2D-descriptors have a deluge of contributions in extracting chemical attributes and they are also capable of representing the 3D molecular features to some extent; although in no case they should be considered as the ultimate one, since they often suffer from the problems of intercorrelation, insufficient chemical information as well as lack of interpretation. However, by following rational approaches, novel 2D-descriptors may be developed to obviate various existing problems giving potential 2D-QSAR equations, thereby solving the innumerable chemical mysteries still unexplored. PMID:25204823
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.
Topological charges in 2D N =(2 ,2 ) theories and massive BPS states
NASA Astrophysics Data System (ADS)
Park, Daniel S.
2015-07-01
We study how charges of global symmetries that are manifest in the ultraviolet definition of a theory are realized as topological charges in its infrared effective theory for two-dimensional theories with N =(2 ,2 ) supersymmetry. We focus on the charges that the states living on S1 carry. The central charge—or Bogomol'nyi-Prasad-Sommerfield (BPS) masses—of the supersymmetry algebra play a crucial role in making this correspondence precise. We study two examples: U (1 ) gauge theories with chiral matter and world-volume theories of "dynamical surface operators" of four-dimensional N =2 gauge theories. In the former example, we show that the flavor charges of the theory are realized as topological winding numbers in the effective theory on the Coulomb branch. In the latter, we show that there is a one-to-one correspondence between topological charges of the effective theory of the dynamical surface operator and the electric, magnetic, and flavor charges of the four-dimensional gauge theory. We also examine the topologically charged massive BPS states on S1 and discover that the massive BPS spectrum is sensitive to the radius of the circle in the simplest theory—the free theory of a periodic twisted chiral field. We clarify this behavior by showing that the massive BPS spectrum on S1, unlike the BPS ground states, cannot be identified as elements of a cohomology.
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.
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.}
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.
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.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.
Cluster Algebras from Dualities of 2d = (2, 2) Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Benini, Francesco; Park, Daniel S.; Zhao, Peng
2015-11-01
We interpret certain Seiberg-like dualities of two-dimensional = (2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kähler moduli space of manifolds constructed from the corresponding Kähler quotients. We study the S 2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor, whose physical origin and consequences we spell out in detail. We also present similar dualities in = (2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.
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.
Untangling tracer trajectories and clarifying coherence in 2D flows using braid theory
NASA Astrophysics Data System (ADS)
Filippi, Margaux; Atis, Séverine; Thiffeault, Jean-Luc; Budišić, Marko; Allshouse, Michael; Peacock, Thomas
2014-11-01
Interpreting ocean surface transport is crucial to many areas of oceanography, ranging from marine ecology to pollution management. To better understand surface mixing, we investigate a braid theory method to detect transport barriers bounding coherent structures in two-dimensional fluid flows. Whereas most existing techniques rely on an extensive spatiotemporal knowledge of the flow field, we seek to identify these structures from sparse data sets involving trajectories of a few tracer particles or floats. We present the results of model and laboratory experimental studies to test the robustness and applicability of the braid theory method, and discuss the potential applicability to oceanic data sets.
Learning control system design based on 2-D theory - An application to parallel link manipulator
NASA Technical Reports Server (NTRS)
Geng, Z.; Carroll, R. L.; Lee, J. D.; Haynes, L. H.
1990-01-01
An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.
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.
NASA Astrophysics Data System (ADS)
Kramer, Patrick L.; Nishida, Jun; Giammanco, Chiara H.; Tamimi, Amr; Fayer, Michael D.
2015-05-01
In nearly all applications of ultrafast multidimensional infrared spectroscopy, the spectral degrees of freedom (e.g., transition frequency) and the orientation of the transition dipole are assumed to be decoupled. We present experimental results which confirm that frequency fluctuations can be caused by rotational motion and observed under appropriate conditions. A theory of the frequency-frequency correlation function (FFCF) observable under various polarization conditions is introduced, and model calculations are found to reproduce the qualitative trends in FFCF rates. The FFCF determined with polarization-selective two-dimensional infrared (2D IR) spectroscopy is a direct reporter of the frequency-rotational coupling. For the solute methanol in a room temperature ionic liquid, the FFCF of the hydroxyl (O-D) stretch decays due to spectral diffusion with different rates depending on the polarization of the excitation pulses. The 2D IR vibrational echo pulse sequence consists of three excitation pulses that generate the vibrational echo, a fourth pulse. A faster FFCF decay is observed when the first two excitation pulses are polarized perpendicular to the third pulse and the echo,
Kramer, Patrick L; Nishida, Jun; Giammanco, Chiara H; Tamimi, Amr; Fayer, Michael D
2015-05-14
In nearly all applications of ultrafast multidimensional infrared spectroscopy, the spectral degrees of freedom (e.g., transition frequency) and the orientation of the transition dipole are assumed to be decoupled. We present experimental results which confirm that frequency fluctuations can be caused by rotational motion and observed under appropriate conditions. A theory of the frequency-frequency correlation function (FFCF) observable under various polarization conditions is introduced, and model calculations are found to reproduce the qualitative trends in FFCF rates. The FFCF determined with polarization-selective two-dimensional infrared (2D IR) spectroscopy is a direct reporter of the frequency-rotational coupling. For the solute methanol in a room temperature ionic liquid, the FFCF of the hydroxyl (O-D) stretch decays due to spectral diffusion with different rates depending on the polarization of the excitation pulses. The 2D IR vibrational echo pulse sequence consists of three excitation pulses that generate the vibrational echo, a fourth pulse. A faster FFCF decay is observed when the first two excitation pulses are polarized perpendicular to the third pulse and the echo, 〈XXY Y〉, than in the standard all parallel configuration, 〈XXXX〉, in which all four pulses have the same polarization. The 2D IR experiment with polarizations 〈XY XY〉 ("polarization grating" configuration) gives a FFCF that decays even more slowly than in the 〈XXXX〉 configuration. Polarization-selective 2D IR spectra of bulk water do not exhibit polarization-dependent FFCF decays; spectral diffusion is effectively decoupled from reorientation in the water system. PMID:25978898
Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation
NASA Astrophysics Data System (ADS)
Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng
2014-05-01
Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.
Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties
NASA Astrophysics Data System (ADS)
Jockers, Hans; Kumar, Vijay; Lapan, Joshua M.; Morrison, David R.; Romo, Mauricio
2012-11-01
The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi-Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models — which we refer to as the PAX and the PAXY model — are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.
On skein relations in class S theories
NASA Astrophysics Data System (ADS)
Tachikawa, Yuji; Watanabe, Noriaki
2015-06-01
Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of the skein relations, that we describe in detail in the case of class S theories of type A. As two applications, we explicitly determine networks corresponding to dyonic loops of super Yang-Mills, and compute the superconformal index of a nontrivial network operator of the T 3 theory.
Beyond classical nucleation theory: A 2-D lattice-gas automata model
NASA Astrophysics Data System (ADS)
Hickey, Joseph
Nucleation is the first step in the formation of a new phase in a thermodynamic system. The Classical Nucleation Theory (CNT) is the traditional theory used to describe this phenomenon. The object of this thesis is to investigate nucleation beyond one of the most significant limitations of the CNT: the assumption that the surface tension of a nucleating cluster of the new phase is independent of the cluster's size and has the same value that it would have in the bulk of the new phase. In order to accomplish this, we consider a microscopic, two-dimensional Lattice Gas Automata (LGA) model of precipitate nucleation in a supersaturated system, with model input parameters Ess (solid particle-to-solid particle bonding energy), Esw (solid particle-to-water particle bonding energy), eta (next-to-nearest neighbour bonding coeffiicent in solid phase), and Cin (initial solute concentration). The LGA method was chosen for its advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system's concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the system's equilibrium concentration. A mean first-passage time (MFPT) technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation are evaluated using a modification to the CNT that incorporates a two-dimensional, radius-dependent surface tension term. The Tolman parameter, delta, which controls the radius-dependence of the surface tension, decreases (increases) as a function of the magnitude of Ess (Esw), at fixed values of eta and Esw (Ess). On the other hand, delta increases as eta increases while E ss and Esw are held constant. The constant surface tension term of the CNT, Sigma0, increases (decreases) with increasing magnitudes of Ess (Esw) fixed values of Esw (Ess), and increases as eta is increased. Together
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.
Note on Gauge Theory on M4 × ZN with Auxiliary Field
NASA Astrophysics Data System (ADS)
Maekawa, T.; Taira, H.
1997-06-01
It is shown that the discrete gauge theory on ZN is well formulated with the auxiliary fields due to Chamseddine et al. and Okumura et al. together with the exterior algebra of Dimakis and Müller-Hoissen. A Lagrangian of the Yang-Mills-Higgs fields is also given.
The structure of the anomalies of gauge theories in the causal approach
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2002-02-01
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based on the Epstein-Glaser approach to renormalization theory. In the case of quantum electrodynamics we obtain quite easily the absence of anomalies in all orders.
Monopoles and knots in skyrme theory.
Cho, Y M
2001-12-17
We show that the Skyrme theory is actually a theory of monopoles which allows a new type of soliton, the topological knot made of the monopole-antimonopole pair, which is different from the well-known skyrmion. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infrared limit. We discuss the physical implications of our results. PMID:11736568
Yang-Mills Magnetofluid Unification
Bambah, Bindu A.; Mahajan, Swadesh M.; Mukku, Chandrasekher
2006-08-18
We generalize the hybrid magnetofluid model of a charged fluid interacting with an electromagnetic field to the dynamics of a relativistic hot fluid interacting with a non-Abelian field. The fluid itself is endowed with a non-Abelian charge and the consequences of this generalization are worked out. Applications of this formalism to the quark gluon plasma are suggested.
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Model of the N-quark potential in SU(N) gauge theory using gauge-string duality
NASA Astrophysics Data System (ADS)
Andreev, Oleg
2016-05-01
We use gauge-string duality to model the N-quark potential in pure Yang-Mills theories. For SU (3), the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the Δ-law at short distances and the Y-law at long distances.
Scale invariance in the causal approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, Dan R.
2001-06-01
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We find the interesting result that, if all fields of the theory have zero masses, then from purely cohomological consideration, one can obtain the anomalous terms of logarithmic type.
N=3 supersymmetric effective action of D2-branes in massive IIA string theory
NASA Astrophysics Data System (ADS)
Go, Gyungchoon; Kwon, O.-Kab; Tolla, D. D.
2012-01-01
We obtain a new type of N=3 Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgs mechanism of the N=3 Gaiotto-Tomasiello theory. This theory has N=1 BPS fuzzy funnel solution, which is expressed in terms of the seven generators of SU(3), excluding T8. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS{sub 5}xS{sup 5}
Hata, Hiroyuki; Miwa, Akitsugu
2006-02-15
We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y{sup i}(s) and two fermionic coordinates {zeta}(s) and {eta}(s) besides the four-dimensional spacetime coordinates x{sup {mu}}(s). We have successfully determined, to quadratic order in {zeta} and {eta}, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS{sub 5}xS{sup 5} background.
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 Astrophysics Data System (ADS)
Buchbinder, I. L.; Ivanov, E. A.; Pletnev, N. G.
2016-05-01
We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang-Mills theory with hypermultiplets and in N = 4 supersymmetric Yang-Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.
Dimensional Reduction of Gauge Theories, Spontaneous Compactification and Model Building
NASA Astrophysics Data System (ADS)
Kubyshin, Yura A.; Mourao, Jose M.; Rudolph, Gerd; Volobujev, Igor P.
This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
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.
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.
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.
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. PMID:27419560
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. PMID:25062163
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.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
Dualities in M-theory and Born-Infeld Theory
Brace, Daniel, M
2001-08-01
We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime.
NASA Astrophysics Data System (ADS)
Geistlinger, Helmut; Ataei-Dadavi, Iman; Mohammadian, Sadjad; Vogel, Hans-Jörg
2015-11-01
We study the impact of pore structure and surface roughness on capillary trapping of nonwetting gas phase during imbibition with water for capillary numbers between 10-7 and 5 × 10-5, within glass beads, natural sands, glass beads monolayers, and 2-D micromodels. The materials exhibit different roughness of the pore-solid interface. We found that glass beads and natural sands, which exhibit nearly the same grain size distribution, pore size distribution, and connectivity, showed a significant difference of the trapped gas phase of about 15%. This difference can be explained by the microstructure of the pore-solid interface. Based on the visualization of the trapping dynamics within glass beads monolayers and 2-D micromodels, we could show that bypass trapping controls the trapping process in glass beads monolayers, while snap-off trapping controls the trapping process in 2-D micromodels. We conclude that these different trapping processes are the reason for the different trapping efficiency, when comparing glass beads packs with natural sand packs. Moreover, for small capillary numbers of 10-6, we found that the cluster size distribution of trapped gas clusters of all 2-D and 3-D porous media can be described by a universal power law behavior predicted from percolation theory. This cannot be expected a priori for 2-D porous media, because bicontinuity of the two bulk phases is violated. Obviously, bicontinuity holds for the thin-film water phase and the bulk gas phase. The snap-off trapping process leads to ordinary bond percolation in front of the advancing bulk water phase and is the reason for the observed universal power law behavior in 2-D micromodels with rough surfaces.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
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.
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.
2004-10-01
A simple and effective method to describe Gaussian beams propagation and diffraction in arbitrary smoothly inhomogeneous 2D medium has been developed based on the eikonal form of complex geometrical optics. The method assumes the eikonal equation can be solved in paraxial approximation in curvilinear frame of references, connected with the central ray. The Riccati-type ordinary differential equation is derived for complex parameter characterizing the Gaussian beam width and phase front curvature. The same parameter was proved to define both the modulus and the argument of the complex amplitude. As a result, the problem of the Gaussian beam diffraction in inhomogeneous media has been reduced to the solution of the ordinary differential equation of the first order, which can be readily calculated numerically for arbitrary profile of dielectric permittivity.
Six-dimensional supergravity on S3 x AdS3 and 2d conformal field theory
de Boer, Jan
1998-06-20
In this paper we study the relation between six-dimensional supergravity compactified on S{sup 3} x AdS{sub 3} and certain two-dimensional conformal field theories. We compute the Kaluza-Klein spectrum of supergravity using representation theory; these methods are quite general and can also be applied to other compactifications involving anti-de Sitter spaces. A detailed comparison between the spectrum of the two-dimensional conformal field theory and supergravity is made, and we find complete agreement. This applies even at the level of certain non-chiral primaries, and we propose a resolution to the puzzle of the missing states recently raised by Vafa. As a further illustration of the method the Kaluza-Klein spectra of F-theory on M{sup 6} x S{sup 3} x AdS{sub 3} and of M-theory on M{sup 6} x S{sup 2} x AdS{sub 3} are computed, with M{sup 6} some Calabi-Yau manifold.
NASA Astrophysics Data System (ADS)
Kh., Lotfy
2012-06-01
In the present paper, we introduce the coupled theory (CD), Lord-Schulman (LS) theory, and Green-Lindsay (GL) theory to study the influences of a magnetic field and rotation on a two-dimensional problem of fibre-reinforced thermoelasticity. The material is a homogeneous isotropic elastic half-space. The method applied here is to use normal mode analysis to solve a thermal shock problem. Some particular cases are also discussed in the context of the problem. Deformation of a body depends on the nature of the force applied as well as the type of boundary conditions. Numerical results for the temperature, displacement, and thermal stress components are given and illustrated graphically in the absence and the presence of the magnetic field and rotation.
Large-N reduction in QCD-like theories with massive adjoint fermions
Azeyanagi, Tatsuo; Hanada, Masanori; Unsal, Mithat; Yacoby, Ran; /Weizmann Inst.
2010-08-26
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.
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…
Harris, R.; Wang, Z.; Liu, Y.
2007-11-19
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
NASA Astrophysics Data System (ADS)
Harris, Rob; Wang, Z. J.; Liu, Yen
2008-01-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
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.
Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
NASA Astrophysics Data System (ADS)
Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia
2016-03-01
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. 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.
Anti-de Sitter-space/conformal-field-theory correspondence and large-N volume independence
Poppitz, Erich; Uensal, Mithat
2010-09-15
We study the Eguchi-Kawai reduction in the strong-coupling domain of gauge theories via the gravity dual of N=4 super-Yang-Mills on R{sup 3}xS{sup 1}. We show that D-branes geometrize volume independence in the center-symmetric vacuum and give supergravity predictions for the range of validity of reduced large-N models at strong coupling.
NASA Technical Reports Server (NTRS)
Weber, M. E.; Dalleska, N. F.; Tjelta, B. L.; Fisher, E. R.; Armentrout, P. B.
1993-01-01
Guided ion-beam mass spectrometry is used to examined the reactions of vibrationally cold ground-state O2(+)(X 2Pi sub g) with H2, D2, and HD. The energy dependence of the absolute integral cross sections from thermal energy to over 4 eV are measured in the center-of-mass frame of reference. Results are also presented for internally excited O2(+) ions reacting with D2 and HD. The results are consistent with the dominant state being the a 4Pi sub u electronic state. The experimental excitation functions are analyzed in detail and interpreted by extending the molecular orbital correlation arguments of Mahan (1971) and by comparison with results of statistical phase space theory and with a theory that predicts a tight transition state.
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.
Solitons and black holes in non-Abelian Einstein-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Dyadichev, V. V.; Gal'tsov, D. V.
2000-08-01
Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.
Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality
NASA Astrophysics Data System (ADS)
Lee, Seungjin; Mafra, Carlos R.; Schlotterer, Oliver
2016-03-01
Recent progress on scattering amplitudes in super Yang-Mills and super-string theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kine-matics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
Valla, Jeffrey; Ceci, Stephen J
2011-03-01
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
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
Saririan, K.
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
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.
SDiff gauge theory and the M2 condensate
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; Townsend, Paul K.
2009-02-01
We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its Script N = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff2 super-Yang-Mills theory describing a condensate of D2-branes.
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. PMID:27363680
New applications of on-shell methods in quantum field theory
NASA Astrophysics Data System (ADS)
Engelund, Oluf Tang
This thesis incorporates 4 years of work: it gives a small introduction to the field of scattering amplitudes and especially into the method of generalized unitarity then discuss 4 different projects all in the field of scattering amplitudes. First we will look at a duality between correlation functions in a special lightlike limit and Wilson loops in N = 4 Super-Yang-Mills. The duality, originally suggested by Alday, Eden, Korchemsky, Maldacena and Sokatchev, was part of a effort to put a firmer footing on the duality between scattering amplitudes and Wilson loops. The duality between correlation functions and Wilson loops does not have any regularization issues (like the other duality) as both have infrared divergences in the specific limits considered. We show how the duality works vertex-by-vertex using just Feynman rules. The method is sufficiently general to allow for extensions of the original duality including operators not taking part in the special light-like limit, other types of operators as well as other theories than N = 4 Super-Yang-Mills. After that we look at how to use generalized unitarity for correlation functions with some examples from N = 4 Super-Yang-Mills. For computations one needs quantities known as form factors which have both asymptotic states like scattering amplitudes and local operators like correlation functions. We compute several form factors using modern methods from scattering amplitudes. Thirdly, we study how to use generalized unitarity for two-dimensional integrable systems. Two-dimensional systems have their own unique set of challenges but generalized unitarity can be adapted to them and we show how one can carry out tests of integrability which would otherwise be difficult. Finally, we look at the 3-dimensional theory known as ABJ(M). Its tree-level amplitudes can be incorporated into a single formula very reminiscent of a result in N = 4 Super-Yang-Mills. Since the result from N = 4 Super-Yang-Mills follow directly from
Classical irregular block, = 2 pure gauge theory and Mathieu equation
NASA Astrophysics Data System (ADS)
Piątek, Marcin; Pietrykowski, Artur R.
2014-12-01
Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.
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.
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.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-03-01
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
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
NASA Astrophysics Data System (ADS)
Feng, Tao; Wang, Jizhe; Tsui, Benjamin M. W.
2016-04-01
The camera of the conventional SPECT system requires a collimator to allow incoming photons from a specific range of incident angle to reach the detector. It is the major factor that determines the spatial resolution of the camera. Moreover, it also greatly reduces the number of detected photons and hence increases statistical fluctuations in the acquired image data. The goal of this paper is to propose a theory and design for a novel high resolution and high sensitivity SPECT system without conventional collimators. The key is to resolve the incident photons from all directional angles and detected by every detector bin. Special ‘attenuators’ were designed to ‘encode’ the incoming photons from different directions similar to coded aperture to form projection data for image reconstruction. Each encoded angular pattern of detected photons was recorded as one measurement. Different angular patterns were achieved by changing the configurations of the attenuators so that angular pattern of different measurements or measurement matrix (MM) is invertible, which guarantee a unique reconstructed image. In simulation, the attenuators were fitted on a virtual full-ring gamma camera, as an alternative to the collimators in conventional SPECT systems. To evaluate the performance of the new SPECT system, analytical simulated projection data in 2D scenario were generated from the XCAT phantom. Noisy simulation using 100 noise realizations suggests that the new attenuator design provides much improved image quality in terms of contrast-noise trade-offs (~30% improvement). The results suggest that the new design of using attenuators to replace collimator is feasible and could potentially improve sensitivity without sacrificing resolution in today’s SPECT systems.
Feng, Tao; Wang, Jizhe; Tsui, Benjamin M W
2016-04-01
The camera of the conventional SPECT system requires a collimator to allow incoming photons from a specific range of incident angle to reach the detector. It is the major factor that determines the spatial resolution of the camera. Moreover, it also greatly reduces the number of detected photons and hence increases statistical fluctuations in the acquired image data. The goal of this paper is to propose a theory and design for a novel high resolution and high sensitivity SPECT system without conventional collimators. The key is to resolve the incident photons from all directional angles and detected by every detector bin. Special 'attenuators' were designed to 'encode' the incoming photons from different directions similar to coded aperture to form projection data for image reconstruction. Each encoded angular pattern of detected photons was recorded as one measurement. Different angular patterns were achieved by changing the configurations of the attenuators so that angular pattern of different measurements or measurement matrix (MM) is invertible, which guarantee a unique reconstructed image. In simulation, the attenuators were fitted on a virtual full-ring gamma camera, as an alternative to the collimators in conventional SPECT systems. To evaluate the performance of the new SPECT system, analytical simulated projection data in 2D scenario were generated from the XCAT phantom. Noisy simulation using 100 noise realizations suggests that the new attenuator design provides much improved image quality in terms of contrast-noise trade-offs (~30% improvement). The results suggest that the new design of using attenuators to replace collimator is feasible and could potentially improve sensitivity without sacrificing resolution in today's SPECT systems. PMID:26976649
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Silva, Guillermo A.
2008-07-01
We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
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{sub 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{sub 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.
NASA Astrophysics Data System (ADS)
Sadri, Darius; Sheikh-Jabbari, Mohammad M.
2006-03-01
We consider Script N = 1, D = 4 superconformal U(N)p × q Yang-Mills theories dual to AdS5 × S5/Zp × Zq orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector of this dilatation operator can be thought of as the transfer matrix for a two-dimensional statistical mechanical system, related to an integrable SU(3) ferromagnetic spin chain system, which in turn is equivalent to a 2+1-dimensional string theory where the spatial slices are discretized on a triangular lattice. This is an extension of the SO(6) spin chain picture of Script N = 4 super Yang-Mills theory. We comment on the integrability of this Script N = 1 gauge theory and hence the corresponding three-dimensional statistical mechanical system, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
2005-08-01
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Microscopic quantum superpotential in Script N = 1 gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
2007-10-01
We consider the Script N = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of Script N = 2 super Yang-Mills theories to the realm of Script N = 1 gauge theories.
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. PMID:14525414
Evidence for large- N phase transitions in mathcal{N}={2^{*}} theory
NASA Astrophysics Data System (ADS)
Russo, Jorge G.; Zarembo, Konstantin
2013-04-01
We solve, using localization, for the large- N master field of {N}={2^{*}} superYang-Mills theory. From that we calculate expectation values of large Wilson loops and the free energy on the four-sphere. At weak coupling, these observables only receive nonperturbative contributions. The analytic solution holds for a finite range of the 't Hooft coupling and terminates at the point of a large- N phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.
Supergrassmannian and large N limit of quantum field theory with bosons and fermions
Konechny, Anatoly; Turgut, O. Teoman
2002-03-01
We study a large N{sub c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.
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.
BCFW recursion relations and string theory
NASA Astrophysics Data System (ADS)
Cheung, Clifford; O'Connell, Donal; Wecht, Brian
2010-09-01
We demonstrate that all tree-level string theory amplitudes can be computed using the BCFW recursion relations. Our proof utilizes the pomeron vertex operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we find that in a particular large complex momentum limit, the asymptotic expansion of massless string amplitudes is identical in form to that of the corresponding field theory amplitudes. This observation makes manifest the fact that field-theoretic Yang-Mills and graviton amplitudes obey KLT-like relations. Moreover, we conjecture that in this large momentum limit certain string theory and field theory amplitudes are identical, and provide evidence for this conjecture. Additionally, we find a new recursion relation which relates tachyon amplitudes to lower-point tachyon amplitudes.
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)
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.
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.
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
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…
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
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.
Phases of a two-dimensional large-N gauge theory on a torus
Mandal, Gautam; Morita, Takeshi
2011-10-15
We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2-dimensional pure Yang-Mills theory on T{sup D+2} with D small radii. The two-dimensional model has various phases characterized by the holonomy of the gauge field around noncontractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method developed in an earlier work (hep-th/0910.4526), which is nonperturbative in the 't Hooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2-dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations. We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.
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}
Schwarzschild Black Holes from Matrix Theory
NASA Astrophysics Data System (ADS)
Banks, T.; Fischler, W.; Klebanov, I. R.; Susskind, L.
1998-01-01
We consider matrix theory compactified on T3 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 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.
NASA Astrophysics Data System (ADS)
Shiramomo, T.; Gao, B.; Mercier, F.; Nishizawa, S.; Nakano, S.; Kakimoto, K.
2014-01-01
The effect of nitrogen and aluminum as doped impurities on the stability of SiC polytypes (C- or Si-face 4H and 6H substrates) formed by physical vapor transport (PVT) was investigated. The stability of the polytypes was analyzed using classical thermodynamic nucleation theory with numerical results obtained from a global model including heat, mass and species transfer in a PVT furnace. The results reveal that the formation of 4H-SiC was more stable than that of 6H-SiC when a grown crystal was doped with nitrogen using C-face 4H- and 6H-SiC as seed crystals. In contrast, formation of 6H-SiC was favored over 4H-SiC when Si-face 4H- and 6H-SiC seed crystals were used. Meanwhile, the formation of 4H-SiC was more stable than that of 6H-SiC when aluminum was the dopant and C- and Si-faces of 6H-SiC were used as seed crystals. Formation of 6H-SiC occurred over that of 4H-SiC in the cases of C- and Si-faces of 4H-SiC as seed crystals.
Probing {N}=2 superconformal field theories with localization
NASA Astrophysics Data System (ADS)
Fiol, Bartomeu; Garolera, Blai; Torrentsa, Genís
2016-01-01
We use supersymmetric localization to study probes of four dimensional Lagrangian {N}=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of {N}=4 supersymmetric Yang-Mills theory.
Ekama, G A; Marais, P
2004-02-01
The applicability of the one-dimensional idealized flux theory (1DFT) for the design of secondary settling tanks (SSTs) is evaluated by comparing its predicted maximum surface overflow (SOR) and solids loading (SLR) rates with that calculated with the two-dimensional computational fluid dynamics model SettlerCAD using as a basis 35 full-scale SST stress tests conducted on different SSTs with diameters from 30 to 45m and 2.25-4.1m side water depth (SWD), with and without Stamford baffles. From the simulations, a relatively consistent pattern appeared, i.e. that the 1DFT can be used for design but its predicted maximum SLR needs to be reduced by an appropriate flux rating, the magnitude of which depends mainly on SST depth and hydraulic loading rate (HLR). Simulations of the Watts et al. (Water Res. 30(9)(1996)2112) SST, with doubled SWDs and the Darvill new (4.1m) and old (2.5m) SSTs with interchanged depths, were run to confirm the sensitivity of the flux rating to depth and HLR. Simulations with and without a Stamford baffle were also performed. While the design of the internal features of the SST, such as baffling, has a marked influence on the effluent SS concentration while the SST is underloaded, these features appeared to have only a small influence on the flux rating, i.e. capacity, of the SST. Until more information is obtained, it would appear from the simulations that the flux rating of 0.80 of the 1DFT maximum SLR recommended by Ekama and Marais (Water Pollut. Control 85(1)(1986)101) remains a reasonable value to apply in the design of full-scale SSTs-for deep SSTs (4m SWD) the flux rating could be increased to 0.85 and for shallow SSTs (2.5m SWD) decreased to 0.75. It is recommended that (i) while the apparent interrelationship between SST flux rating and depth suggests some optimization of the volume of the SST, this be avoided and (ii) the depth of the SST be designed independently of the surface area as is usually the practice and once selected, the
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
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.
Sasakian quiver gauge theories and instantons on the conifold
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.; Lechtenfeld, Olaf; Popov, Alexander D.; Szabo, Richard J.
2016-06-01
We consider Spin (4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form Md ×T 1 , 1, where Md is a smooth manifold and T 1 , 1 is a five-dimensional Sasaki-Einstein manifold Spin (4) / U (1). We obtain new quiver gauge theories on Md extending those induced via reduction over the leaf spaces CP1 × CP1 in T 1 , 1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin (4)-equivariant instantons on the conifold which is realized as the metric cone over T 1 , 1. We give an explicit construction of these moduli spaces as Kähler quotients.
NASA Astrophysics Data System (ADS)
Rey, Soo-Jong; Suyama, Takao
2011-01-01
Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in mathcal{N} = 2 superconformal (quiver) gauge theories in the large number limit of colors. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in mathcal{N} = 4 super Yang-Mills theory with respect to `t Hooft coupling. For theory with gauge group SU( N) coupled to 2 N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth — at most, it can grow as a power of `t Hooft coupling. For theory with gauge group SU( N)×SU( N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in mathcal{N} = 4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of the two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loops in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both classes of theory holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicates that holographic dual of these gauge theories is provided by certain non-critical string theories.
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.
Dynamic universality class of large-N gauge theories
Natsuume, Makoto; Okamura, Takashi
2011-02-15
In dynamic critical phenomena, singular behaviors appear not only in the order parameter but also in the other transport coefficients (due to the mode-mode coupling). However, this effect has not been observed in the AdS/CFT duality. We point out that this mode-mode coupling is suppressed by 1/N{sup 2} in the large-N gauge theories which correspond to model H in the classification of Hohenberg and Halperin. Thus, the effect cannot be seen in the classical supergravity approximation. We illustrate this point using the example of the N=4 super-Yang-Mills theory at a finite chemical potential. We also discuss the implications of this result to heavy-ion collisions.
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
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.
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.
Anti-De Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
NASA Astrophysics Data System (ADS)
Witten, Edward
2014-03-01
The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.
Next-to-simplest quantum field theories
NASA Astrophysics Data System (ADS)
Lal, Shailesh; Raju, Suvrat
2010-05-01
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-15
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
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…
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-04-01
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.
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.
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
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.
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.
Baby universes in string theory
Dijkgraaf, Robbert; Gopakumar, Rajesh; Ooguri, Hirosi; Vafa, Cumrun
2006-03-15
We argue that the holographic description of four-dimensional Bogomol'nyi-Prasad-Sommerfield black holes naturally includes multicenter solutions. This suggests that the holographic dual to the gauge theory is not a single AdS{sub 2}xS{sup 2} but a coherent ensemble of them. We verify this in a particular class of examples, where the two-dimensional Yang-Mills theory gives a holographic description of the black holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic formulation, we show that O(e{sup -N}) nonperturbative effects entangle the two Fermi surfaces. In an Euclidean description, the wave function of the multicenter black holes gets mapped to the Hartle-Hawking wave function of baby universes. This provides a concrete realization, within string theory, of effects that can be interpreted as the creation of baby universes. We find that, at least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments.
Stability of D brane-anti D brane systems in confining gauge theories
NASA Astrophysics Data System (ADS)
Ghoroku, Kazuo; Nakamura, Akihiro; Toyoda, Fumihiko
2011-01-01
We study the stability of a special form of D brane embedding which is regarded as a bound state of D n and anti-D n brane embedded in a 10D supergravity background which is dual to a confining gauge theory. For D5 branes with U(1) flux, their bound-state configuration can be regarded as the baryonium vertex. For D branes of n=6 and 8 without the U(1) flux, their bound states have been used to introduce flavor quarks in the dual supersymmetric Yang-Mills theory. In any case, it would be important to ensure that they are free from tachyon instability. For all these cases, we could show their stability with respect to this point.
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.
Hyperkähler sigma model and field theory on Gibbons-Hawking spaces
NASA Astrophysics Data System (ADS)
Dey, Anindya; Neitzke, Andrew
2014-04-01
We describe a novel deformation of the 3-dimensional sigma model with hyperkähler target, which arises naturally from the compactification of a 4-dimensional = 2 theory on a hyperkähler circle bundle (Gibbons-Hawking space). We derive the condition for which the deformed sigma model preserves 4 out of the 8 supercharges. We also study the contribution from a NUT center to the sigma model path integral, and find that supersymmetry implies it is a holomorphic section of a certain holomorphic line bundle over the hyperkähler target. We study explicitly the case where the original 4-dimensional theory is pure U(1) super Yang-Mills, and show that the contribution from a NUT center in this case is simply the Jacobi theta function.
NASA Astrophysics Data System (ADS)
Mayor, Louise
2016-05-01
Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.
NASA Astrophysics Data System (ADS)
Eto, Minoru; Murakami, Yoshihide
2015-03-01
Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.
Cohomology Methods in Causal Perturbation Theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2010-01-01
Various problems in perturbation theory of (quantum) gauge models can be rephrased in the language of cohomology theory. This was already noticed in the functional formulation of perturbative gauge theories. Causal perturbation theory is a fully quantum approach: is works only with the chronological products which are defined as operator-valued distributions in the Fock space of the model. The use of causal perturbation theory leads to similar cohomology problems; the main difference with respect to the functional methods comes from the fact that the gauge transformation of the causal approach is, essentially, the linear part of the non-linear BRST transformation. Using these methods it is possible to give a nice determination of the interaction Lagrangians for gauge models (Yang-Mills and gravitation in the linear approximation); one obtains with this method the unicity of the interaction Lagrangian up to trivial terms. The case of quantum gravity is highly non-trivial and can be generalized with this method to the massive graviton case. Going to higher orders of perturbation theory one finds quantum anomalies. Again the cohomological methods can be used to determine the generic form of these anomalies. Finally, one can investigate the arbitrariness of the chronological products in higher orders and reduce this problem to cohomology methods also.
2001-01-31
This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.
Integrable theories in any dimension: a perspective
Alvarez, Orlando; Ferreira, L. A.
1999-07-13
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of dimension d+1 by the introduction of a d-form connection. The method has been used to study several theories of physical interest, like self-dual Yang-Mills theories, Bogomolny equations, non-linear sigma models and Skyrme-type models. The local version of the generalized zero curvature involves a Lie algebra and a representation of it, leading to a number of conservation laws equal to the dimension of that representation. We discuss the conditions a given theory has to satisfy in order for its associated zero curvature to admit an infinite dimensional (reducible) representation. We also present the theory in the more abstract setting of the space of loops, which gives a deeper understanding and a more simple formulation of integrability in any dimension.
Thermodynamics of theories with sixteen supercharges in non-trivial vacua
NASA Astrophysics Data System (ADS)
Grignani, Gianluca; Griguolo, Luca; Mori, Nicola; Seminara, Domenico
2007-10-01
We study the thermodynamics of maximally supersymmetric U(N) Yang-Mills theory on Bbb R × S2 at large N. The model arises as a consistent truncation of Script N = 4 super Yang-Mills on Bbb R × S3 and as the continuum limit of the plane-wave matrix model expanded around the N spherical membrane vacuum. The theory has an infinite number of classical BPS vacua, labeled by a set of monopole numbers, described by dual supergravity solutions. We first derive the Lagrangian and its supersymmetry transformations as a deformation of the usual dimensional reduction of Script N = 1 gauge theory in ten dimensions. Then we compute the partition function in the zero 't Hooft coupling limit in different monopole backgrounds and with chemical potentials for the R-charges. In the trivial vacuum we observe a first-order Hagedorn transition separating a phase in which the Polyakov loop has vanishing expectation value from a regime in which this order parameter is non-zero, in analogy with the four-dimensional case. The picture changes in the monopole vacua due to the structure of the fermionic effective action. Depending on the regularization procedure used in the path integral, we obtain two completely different behaviors, triggered by the absence or the appearance of a Chern-Simons term. In the first case we still observe a first-order phase transition, with Hagedorn temperature depending on the monopole charges. In the latter the large N behavior is obtained by solving a unitary multi-matrix model with a peculiar logarithmic potential, the system does not present a phase transition and it always appears in a ``deconfined'' phase.
Nanoimprint lithography: 2D or not 2D? A review
NASA Astrophysics Data System (ADS)
Schift, Helmut
2015-11-01
Nanoimprint lithography (NIL) is more than a planar high-end technology for the patterning of wafer-like substrates. It is essentially a 3D process, because it replicates various stamp topographies by 3D displacement of material and takes advantage of the bending of stamps while the mold cavities are filled. But at the same time, it keeps all assets of a 2D technique being able to pattern thin masking layers like in photon- and electron-based traditional lithography. This review reports about 20 years of development of replication techniques at Paul Scherrer Institut, with a focus on 3D aspects of molding, which enable NIL to stay 2D, but at the same time enable 3D applications which are "more than Moore." As an example, the manufacturing of a demonstrator for backlighting applications based on thermally activated selective topography equilibration will be presented. This technique allows generating almost arbitrary sloped, convex and concave profiles in the same polymer film with dimensions in micro- and nanometer scale.
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.
2D constant-loss taper for mode conversion
NASA Astrophysics Data System (ADS)
Horth, Alexandre; Kashyap, Raman; Quitoriano, Nathaniel J.
2015-03-01
Proposed in this manuscript is a novel taper geometry, the constant-loss taper (CLT). This geometry is derived with 1D slabs of silicon embedded in silicon dioxide using coupled-mode theory (CMT). The efficiency of the CLT is compared to both linear and parabolic tapers using CMT and 2D finite-difference time-domain simulations. It is shown that over a short 2D, 4.45 μm long taper the CLT's mode conversion efficiency is ~90% which is 10% and 18% more efficient than a 2D parabolic or linear taper, respectively.
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.
NASA Astrophysics Data System (ADS)
Noronha, Jorge
2010-02-01
We show that in four-dimensional gauge theories dual to five-dimensional Einstein gravity coupled to a single scalar field in the bulk, the derivative of the single heavy quark free energy in the deconfined phase is dFQ(T)/dT˜-1/cs2(T), where cs(T) is the speed of sound. This general result provides a direct link between the softest point in the equation of state of strongly-coupled plasmas and the deconfinement phase transition described by the expectation value of the Polyakov loop. We give an explicit example of a gravity dual with black hole solutions that can reproduce the lattice results for the expectation value of the Polyakov loop and the thermodynamics of SU(3) Yang-Mills theory in the (nonperturbative) temperature range between Tc and 3Tc.
Gauge theories on noncommutative ℂPN and Bogomol'nyi-Prasad-Sommerfield-like equations
NASA Astrophysics Data System (ADS)
Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi
2015-11-01
We give the Fock representation of a noncommutative ℂPN and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ℂPN. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Bogomol'nyi-Prasad-Sommerfield (BPS)-like equations on noncommutative ℂP1 and ℂP2 are derived from these actions. There are analogies between BPS-like equations on ℂP1 and monopole equations on ℝ3 and BPS-like equations on ℂP2 and instanton equations on ℝ8. We discuss solutions of these BPS-like equations.
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.
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.
Torus Knot Polynomials and Susy Wilson Loops
NASA Astrophysics Data System (ADS)
Giasemidis, Georgios; Tierz, Miguel
2014-12-01
We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.
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.
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.
Cosmologies with null singularities and their gauge theory duals
Das, Sumit R.; Michelson, Jeremy; Narayan, K.; Trivedi, Sandip P.
2007-01-15
We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in S. R. Das, J. Michelson, K. Narayan, S. P. Trivedi, hep-th/0602107. The dual theory is a deformed N=4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a lightlike direction. We concentrate on backgrounds which become AdS{sub 5}xS{sup 5} at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the matrix membrane theory which describes these pp-wave backgrounds.
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
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 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.
Interpolating the Coulomb phase of little string theory
NASA Astrophysics Data System (ADS)
Lin, Ying-Hsuan; Shao, Shu-Heng; Wang, Yifan; Yin, Xi
2015-12-01
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. We also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2 , 0) little string theory.
Regularized path integrals and anomalies: U(1) chiral gauge theory
NASA Astrophysics Data System (ADS)
Kopper, Christoph; Lévêque, Benjamin
2012-02-01
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Geometric features of string theory at low-energy
NASA Astrophysics Data System (ADS)
Lukic, Sergio
In this thesis we study several differential-geometric aspects of the low energy limit of string theory. We focus on anomaly cancellation issues in M-theory on a manifold with boundary and background fluxes, and the computation of non-holomorphic quantities in Calabi-Yau compactifications. In the first chapter we introduce the motivation and the problems that we will study. In the second chapter we show how the coupling of gravitinos and gauginos to fluxes modifies anomaly cancellation in M-theory on a manifold with boundary. Anomaly cancellation continues to hold, after a shift of the definition of the gauge currents by a local gauge invariant expression in the curvatures and E8 fieldstrengths. We compute the first nontrivial correction of this kind. In the last chapter, we introduce methods to determine the form of the effective four-dimensional field theory corresponding to compactifications of string theory. More precisely, we develop iterative methods for finding solutions to the Ricci flat equations on a Calabi-Yau variety, and to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas developed by Donaldson. Finally, we show how these techniques can be understood using the language of geometric quantization of Kaehler manifolds, and suggest how one can use these ideas to explicitly construct additional geometric objects.
2D induced gravity from the canonically gauged WZNW system
NASA Astrophysics Data System (ADS)
Blagojević, M.; Popović, D. S.; Sazdović, B.
1999-02-01
Starting from the Kac-Moody structure of the WZNW model for SL(2,R) and using the general canonical formalism, we formulate a gauge theory invariant under local SL(2,R)×SL(2,R) and diffeomorphisms. This theory represents a gauge extension of the WZNW system, defined by a difference of two simple WZNW actions. By performing a partial gauge fixing and integrating out some dynamical variables, we prove that the resulting effective theory coincides with the induced gravity in 2D. The geometric properties of the induced gravity are obtained out of the gauge properties of the WZNW system with the help of the Dirac brackets formalism.
Phase Engineering of 2D Tin Sulfides.
Mutlu, Zafer; Wu, Ryan J; Wickramaratne, Darshana; Shahrezaei, Sina; Liu, Chueh; Temiz, Selcuk; Patalano, Andrew; Ozkan, Mihrimah; Lake, Roger K; Mkhoyan, K A; Ozkan, Cengiz S
2016-06-01
Tin sulfides can exist in a variety of phases and polytypes due to the different oxidation states of Sn. A subset of these phases and polytypes take the form of layered 2D structures that give rise to a wide host of electronic and optical properties. Hence, achieving control over the phase, polytype, and thickness of tin sulfides is necessary to utilize this wide range of properties exhibited by the compound. This study reports on phase-selective growth of both hexagonal tin (IV) sulfide SnS2 and orthorhombic tin (II) sulfide SnS crystals with diameters of over tens of microns on SiO2 substrates through atmospheric pressure vapor-phase method in a conventional horizontal quartz tube furnace with SnO2 and S powders as the source materials. Detailed characterization of each phase of tin sulfide crystals is performed using various microscopy and spectroscopy methods, and the results are corroborated by ab initio density functional theory calculations. PMID:27099950
Perspectives for spintronics in 2D materials
NASA Astrophysics Data System (ADS)
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
On the superconformal index of Argyres-Douglas theories
NASA Astrophysics Data System (ADS)
Buican, Matthew; Nishinaka, Takahiro
2016-01-01
We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the ({A}1,{A}2n-3) and the ({A}1,{D}2n) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain {N}=2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the ({A}1,{A}2n-3) and ({A}1,{D}2n) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class {S} construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the ({A}1,{A}3) and ({A}1,{D}4) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S 1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S 1 reduction of our indices in a separate paper.
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.
Nonholomorphic corrections from three-branes in F theory
NASA Astrophysics Data System (ADS)
de Mello Koch, Robert; Paulin-Campbell, Alastair; Rodrigues, João P.
1999-11-01
We construct solutions of type IIB supergravity corresponding to seven-branes, an O7 plane, and three-branes. By considering a probe moving in this background, with constant coupling and an AdS5 component in its geometry, we are able to reproduce the exact low energy effective action for N=2 super Yang-Mills theory with gauge group SU(2) and Nf=4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS5 geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behavior of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. We study how these instanton corrections are reflected in the background geometry by calculating the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action is in complete agreement with field theory expectations.
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)
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.
Large-N volume independence in conformal and confining gauge theories
Unsal, Mithat; Yaffe, Laurence G.; /Washington U., Seattle
2010-08-26
Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on R{sup d-k} x (S{sup 1}){sup k} are independent of the S{sup 1} radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on R{sup d}, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on R{sup d-k} x (S{sup 1}){sup k}. In other words, finite volume effects are 1/N suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In N = 4 supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on R{sup 4-k} x (S{sup 1}){sup k} has a moduli space which contains points with all possible realizations of center symmetry. Large N QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.
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.
2D imaging of functional structures in perfused pig heart
NASA Astrophysics Data System (ADS)
Kessler, Manfred D.; Cristea, Paul D.; Hiller, Michael; Trinks, Tobias
2002-06-01
In 2000 by 2D-imaging we were able for the first time to visualize in subcellular space functional structures of myocardium. For these experiments we used hemoglobin-free perfused pig hearts in our lab. Step by step we learned to understand the meaning of subcellular structures. Principally, the experiment revealed that in subcellular space very fast changes of light scattering can occur. Furthermore, coefficients of different parameters were determined on the basis of multicomponent system theory.
Variational Study of SU(3) Gauge Theory by Stationary Variance
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2015-07-01
The principle of stationary variance is advocated as a viable variational approach to gauge theories. The method can be regarded as a second-order extension of the Gaussian Effective Potential (GEP) and seems to be suited for describing the strong-coupling limit of non-Abelian gauge theories. The single variational parameter of the GEP is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of coupled integral equations. The stationary conditions can be easily derived by the self-energy, without having to write the effective potential, making use of a general relation between self-energy and functional derivatives that has been proven to any order. The low- energy limit of pure Yang-Mills SU(3) gauge theory has been studied in Feynman gauge, and the stationary equations are written as integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.
Noncommutative gauge theory and symmetry breaking in matrix models
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2010-04-15
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3){sub c}xSU(2){sub L}xU(1){sub Q}[resp. SU(3){sub c}xU(1){sub Q}], which couples appropriately to all fields in the standard model. An additional U(1){sub B} gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.
N=2, 4 supersymmetric gauge field theory in two-time physics
Bars, Itzhak; Kuo, Y.-C.
2009-01-15
In the context of two-time physics in 4+2 dimensions we construct the most general N=2, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. When the equations of motion are used the SUSY transformations close to the supergroup SU(2,2|N) with N=1, 2, 4. The SU(2,2)=SO(4,2) subsymmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1, 2, 4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for nonperturbative or exact solutions of these theories.
Light field morphing using 2D features.
Wang, Lifeng; Lin, Stephen; Lee, Seungyong; Guo, Baining; Shum, Heung-Yeung
2005-01-01
We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field. PMID:15631126
2D materials for nanophotonic devices
NASA Astrophysics Data System (ADS)
Xu, Renjing; Yang, Jiong; Zhang, Shuang; Pei, Jiajie; Lu, Yuerui
2015-12-01
Two-dimensional (2D) materials have become very important building blocks for electronic, photonic, and phononic devices. The 2D material family has four key members, including the metallic graphene, transition metal dichalcogenide (TMD) layered semiconductors, semiconducting black phosphorous, and the insulating h-BN. Owing to the strong quantum confinements and defect-free surfaces, these atomically thin layers have offered us perfect platforms to investigate the interactions among photons, electrons and phonons. The unique interactions in these 2D materials are very important for both scientific research and application engineering. In this talk, I would like to briefly summarize and highlight the key findings, opportunities and challenges in this field. Next, I will introduce/highlight our recent achievements. We demonstrated atomically thin micro-lens and gratings using 2D MoS2, which is the thinnest optical component around the world. These devices are based on our discovery that the elastic light-matter interactions in highindex 2D materials is very strong. Also, I would like to introduce a new two-dimensional material phosphorene. Phosphorene has strongly anisotropic optical response, which creates 1D excitons in a 2D system. The strong confinement in phosphorene also enables the ultra-high trion (charged exciton) binding energies, which have been successfully measured in our experiments. Finally, I will briefly talk about the potential applications of 2D materials in energy harvesting.
Inertial solvation in femtosecond 2D spectra
NASA Astrophysics Data System (ADS)
Hybl, John; Albrecht Ferro, Allison; Farrow, Darcie; Jonas, David
2001-03-01
We have used 2D Fourier transform spectroscopy to investigate polar solvation. 2D spectroscopy can reveal molecular lineshapes beneath ensemble averaged spectra and freeze molecular motions to give an undistorted picture of the microscopic dynamics of polar solvation. The transition from "inhomogeneous" to "homogeneous" 2D spectra is governed by both vibrational relaxation and solvent motion. Therefore, the time dependence of the 2D spectrum directly reflects the total response of the solvent-solute system. IR144, a cyanine dye with a dipole moment change upon electronic excitation, was used to probe inertial solvation in methanol and propylene carbonate. Since the static Stokes' shift of IR144 in each of these solvents is similar, differences in the 2D spectra result from solvation dynamics. Initial results indicate that the larger propylene carbonate responds more slowly than methanol, but appear to be inconsistent with rotational estimates of the inertial response. To disentangle intra-molecular vibrations from solvent motion, the 2D spectra of IR144 will be compared to the time-dependent 2D spectra of the structurally related nonpolar cyanine dye HDITCP.
Internal Photoemission Spectroscopy of 2-D Materials
NASA Astrophysics Data System (ADS)
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
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.
Breakdown of wave diffusion in 2D due to loops.
Haney, Matthew; Snieder, Roel
2003-08-29
The validity of the diffusion approximation for the intensity of multiply scattered waves is tested with numerical simulations in a strongly scattering 2D medium of finite extent. We show that the diffusion equation underestimates the intensity and attribute this to both the neglect of recurrent scattering paths and interference within diffusion theory. We present a theory to quantify this discrepancy based on counting all possible scattering paths between point scatterers. Interference phenomena, due to loop paths, are incorporated in a way similar to coherent backscattering. PMID:14525183
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.
2D electronic materials for army applications
NASA Astrophysics Data System (ADS)
O'Regan, Terrance; Perconti, Philip
2015-05-01
The record electronic properties achieved in monolayer graphene and related 2D materials such as molybdenum disulfide and hexagonal boron nitride show promise for revolutionary high-speed and low-power electronic devices. Heterogeneous 2D-stacked materials may create enabling technology for future communication and computation applications to meet soldier requirements. For instance, transparent, flexible and even wearable systems may become feasible. With soldier and squad level electronic power demands increasing, the Army is committed to developing and harnessing graphene-like 2D materials for compact low size-weight-and-power-cost (SWAP-C) systems. This paper will review developments in 2D electronic materials at the Army Research Laboratory over the last five years and discuss directions for future army applications.
2-d Finite Element Code Postprocessor
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 forcesmore » 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.« less
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. PMID:27478083
Geometry and topology of bubble solutions from gauge theory
NASA Astrophysics Data System (ADS)
Chen, Heng-Yu; Correa, Diego H.; Silva, Guillermo A.
2007-07-01
We study how geometrical and topological aspects of certain (1)/(2)-BPS type IIB supergravity solutions are captured by the N=4 super Yang-Mills gauge theory in the AdS/CFT context. The type IIB solutions are completely characterized by arbitrary droplets in a plane and we consider, in particular, concentric droplets. We probe the dual (1)/(2)-BPS operators of the gauge theory with single traces and extract their one-loop anomalous dimensions. The action of the one-loop dilatation operator can be reformulated as the Hamiltonian of a bosonic lattice. The operators defining the Hamiltonian encode the topology of the droplet. The axial symmetry of the droplets turns out to be essential for obtaining the spectrum of the Hamiltonians. In appropriate BMN limits, the near-BPS spectrum reproduces the spectrum of near-BPS string excitations propagating along each individual edge of the droplet of the dual geometric background. We also study semiclassical regimes for the Hamiltonians. We show that, for droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.