Four-dimensional Gauge Theories Research Articles

Electromagnetic response in supersymmetric Yang-Mills fluid

Supersymmetric Yang-Mills theory is an example of a four-dimensional gauge theory where thermal current-current spectral functions can be calculated analytically at both weak and strong coupling. This allows one to track how electromagnetic response quantities such as photon production rate and electrical conductivity change as the coupling varies from the perturbative g 2 N c ≪ 1 to the non-perturbative g 2 N c → ∞ regime. We discuss potential lessons which may be drawn for QCD.

Dynamical stabilization of runaway potentials at finite density

We study four-dimensional non-Abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of a chemical potential generates non-Abelian field strength condensates. These condensates are homogeneous but non-isotropic. The end point of the condensation process is a stable homogeneous, but non-isotropic, vacuum in which both gauge and flavor symmetries and the rotational invariance are spontaneously broken. Possible applications of this phenomenon for the gauge theory/string theory correspondence and in cosmology are briefly discussed.

Gravity duals to deformed SYM theories and generalized complex geometry

We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of N =4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.

Wilson-’t Hooft operators in four-dimensional gauge theories andS-duality

We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-'t Hooft operators, since in the purely electric case they reduce to the well-known Wilson loops, while in general they may carry 't Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on AdS^2\times S^2. We show that Wilson-'t Hooft operators are classifed by a pair of weights (electric and magnetic) for the gauge group and its magnetic dual, modulo the action of the Weyl group. If the magnetic weight does not belong to the coroot lattice of the gauge group, the corresponding operator is topologically nontrivial (carries nonvanishing 't Hooft magnetic flux). We explain how the spectrum of Wilson-'t Hooft operators transforms under the shift of the theta-angle by 2\pi. We show that, depending on the gauge group, either SL(2,Z) or one of its congruence subgroups acts in a natural way on the set of Wilson-'t Hooft operators. This can be regarded as evidence for the S-duality of N=4 super-Yang-Mills theory. We also compute the one-point function of the stress-energy tensor in the presence of a Wilson-'t Hooft operator at weak coupling.

TRANSVERSE WARD–TAKAHASHI RELATION FOR THE FERMION–BOSON VERTEX TO ONE-LOOP ORDER

In this paper, the transverse Ward–Takahashi relation for the fermion–boson vertex in momentum space is derived in four-dimensional Abelian gauge theory. We show that, by a formal derivation, the transverse Ward–Takahashi relation to one-loop order is satisfied. We also calculate the transverse Ward–Takahashi relation to one-loop order in an arbitrary covariant gauge in the case of massless fermions and find that the result is exactly the same as we obtain in terms of the one-loop fermion–boson vertex calculated in perturbation theory by using Feynman rules. This provides an approach to determine the transverse part of the vertex.

Diffusion model forSU(N)QCD screening

We consider a phenomenological model for the dynamics of Wilson loops in pure SU(N) QCD where the expectation value of the loop is the average over an interacting diffusion process on the group manifold SU(N). The interaction is provided by an arbitrary potential that generates the transition from the Casimir scaling regime into the screening phase of the four-dimensional gauge theory. The potential is required to respect the underlying center symmetry of the gauge theory, and this predicts screening of arbitrary SU(N) representations to the corresponding antisymmetric representations of the same N-ality. The stable strings before the onset of screening are therefore the k strings. In the process we find a nontrivial but solvable modification of the QCD{sub 2} matrix model that involves an arbitrary potential.

Quantization of the Chern invariant polynomial and its topological quantum ground state

The symplectic quantization of the Chern invariant polynomial on a 2 n-dimensional manifold is considered. The ground state wave functional as a representation of the vacuum state of the theory is constructed in terms of the Chern-Simons form. An important consequence of these results is that the existence of the Chern-Simons wave functional is not exclusive of topological four-dimensional gauge theory.

Coherent topological charge structure inCPN−1models and QCD

In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional $C{P}^{N\ensuremath{-}1}$ sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long-range topological structure found in $C{P}^{N\ensuremath{-}1}$ and the observed sign coherence along three-dimensional sheets in four-dimensional QCD gauge configurations. In both cases, coherent regions of topological charge form along membranelike surfaces of codimension one. We show that the Monte Carlo results, for both two-dimensional and four-dimensional gauge theory, support a view of topological charge fluctuations suggested by L\"uscher and Witten. In this framework, the observed membranes are associated with boundaries between ``k-vacua,'' characterized by an effective local value of $\ensuremath{\theta}$ which jumps by $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$ across the boundary.

Clash of positivities in topological density correlators

We discuss the apparent conflict between reflection positivity and positivity of the topological susceptibility in two-dimensional nonlinear sigma models and in four-dimensional gauge theories. We pay special attention to the fact that this apparent conflict is already present on the lattice; its resolution puts some nontrivial restrictions on the short-distance behavior of the lattice correlator. It is found that these restrictions can be satisfied both in the case of asymptotic freedom and the dissident scenario of a critical point at finite coupling.

Non-critical superstrings from four-dimensional gauge theory

We study large-N double-scaling limits of U(N) gauge theories in four dimensions. We focus on theories in a partially confining phase where an abelian subgroup $\hat{G}$ of the gauge group remains unconfined. Double-scaling is defined near critical points in the parameter/moduli space where states charged under $\hat{G}$ become massless. In specific cases, we present evidence that the double-scaled theory is dual to a non-critical superstring background. Models studied include the $\beta$-deformation of ${\cal N}=4$ SUSY Yang-Mills which leads to a non-critical string theory with sixteen supercharges. We also study ${\cal N}=1$ SUSY Yang-Mills theory coupled to a single chiral superfield with a polynomial superpotential which leads to a related string theory with eight supercharges. In both cases the string coupling is small and the background is free from Ramond-Ramond flux.

Transport properties of cascading gauge theories

Cascading gauge theories of Klebanov et al. provide a model within a framework of gauge theory/string theory duality for a four-dimensional nonconformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description, we study sound wave propagation in strongly coupled cascading gauge theory plasma. We analytically compute the speed of sound and the bulk viscosity of cascading gauge theory plasma at a temperature much larger than the strong coupling scale of the theory. The sound wave dispersion relation is obtained from the hydrodynamic pole in the stress-energy tensor two-point correlation function. The speed of sound extracted from the pole of the correlation function agrees with its value computed in Phys. Rev. D 72, 066003 (2005), using the equation of state. We find that the bulk viscosity of the hot cascading gauge theory plasma is nonzero at the leading order in the deviation from conformality.

Review Article

In this work we review recent progress in four-dimensional conformal quantum field theories and scaling dimensions of local operators. Here we consider the example of maximally supersymmetric gauge theory and present techniques to derive, investigate and apply the dilatation operator which measures the scaling dimensions. We construct the dilatation operator by purely algebraic means: Relying on the symmetry algebra and structural properties of Feynman diagrams we are able to bypass involved, higher-loop field theory computations. In this way we obtain the complete one-loop dilatation operator and the planar, three-loop deformation in an interesting subsector. These results allow us to address the issue of integrability within a planar four-dimensional gauge theory: We prove that the complete dilatation generator is integrable at one loop and present the corresponding Bethe ansatz. We furthermore argue that integrability extends to three loops and beyond. Assuming that it holds indeed, we finally construct a novel spin chain model at five loops and propose a Bethe ansatz which might be valid at arbitrary loop order!

Formula omitted] hydrodynamics

Using gauge theory/string theory correspondence certain universal aspects of the strongly coupled four-dimensional gauge theory hydrodynamics were established in hep-th/0311175. The analysis was performed in the framework of “membrane paradigm” approach to the fluctuations on the black brane stretched horizon. We confirm the universal result for the shear viscosity to the entropy density ratio for the strongly coupled N = 2 * gauge theory from explicit computation of the finite temperature Minkowski-space correlation functions in the dual supergravity geometry.

Vortex Strings and Four-Dimensional Gauge Dynamics

We study the low-energy quantum dynamics of vortex strings in the Higgs phase of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is shown to coincide with the BPS spectrum of the four-dimensional parent gauge theory. Perturbative string excitations correspond to bound W-bosons and quarks while the monopoles appear as kinks on the vortex string. This provides a physical explanation for an observation by N. Dorey relating the quantum spectra of theories in two and four dimensions.

An approach to higher dimensional theories based on lattice gauge theory

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram.

Towards the deconstruction of M-theory

We argue that there is an equivalence of M-theory on T^3 \times A_{N-1} with a four-dimensional non-supersymmetric quiver gauge theory on the Higgs branch. The quiver theory in question has gauge group SU(N)^{N_4N_6N_8} and is considered in a strong coupling and large N_{4,6,8} limit. We provide field- and string-theoretical evidence for the equivalence making use of the deconstruction technique. In particular, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies.

The holographic supercurrent anomaly

The γ-trace anomaly of supersymmetry current in a supersymmetric gauge theory shares a superconformal anomaly multiplet with the chiral R-symmetry anomaly and the Weyl anomaly, and its holographic reproduction is a valuable test to the AdS/CFT correspondence conjecture. We investigate how the γ-trace anomaly of the supersymmetry current of N=1 four-dimensional supersymmetric gauge theory in an N=1 conformal supergravity background can be extracted out from the N=2 gauged supergravity in five dimensions. It is shown that the reproduction of this super-Weyl anomaly originates from the following two facts: first the N=2 bulk supersymmetry transformation converts into N=1 superconformal transformation on the boundary, which consists of N=1 supersymmetry transformation and special conformal supersymmetry (or super-Weyl) transformation; second the supersymmetry variation of the bulk action of five-dimensional gauged supergravity is a total derivative. The non-compatibility of supersymmetry and the super-Weyl transformation invariance yields the holographic supersymmetry current anomaly. Furthermore, we speculate on that the contribution from the external gauge and gravitational background fields to the superconformal anomaly may have different holographic origin.

On the relation between effective supersymmetric actions in different dimensions

We make two remarks: (i) Renormalization of the effective charge in a four-dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum-mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this gives us a simple proof of nonrenormalization theorems for the original four-dimensional theory. (ii) We establish a nontrivial relationship between the effective (0 + 1)-dimensional and (1 + 1)-dimensional Lagrangians. (The latter represent conventional Kählerian σ models.)

Supersymmetric gauge theories on noncommutative superspace

We study four-dimensional supersymmetric gauge theory on the noncommutative superspace. We construct the gauge-invariant action of N=1 super-Yang–Mills theory with chiral and antichiral superfields, which has N=12 supersymmetry on the noncommutative superspace. We also construct the action of N=2 super-Yang–Mills theory. It is shown that this theory has only N=12 supersymmetry.

Monopoles, affine algebras and the gluino condensate

We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly coupled way for a small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c2, the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. For gauge groups SU(N), SO(N) and USp(2N) our results for the gluino condensate are in precise agreement with the “weak coupling instanton” expressions (and not with the “strong coupling instanton” calculations). For the exceptional gauge groups we calculate the values of the gluino condensate for the first time.