Four-dimensional Gauge Theories Research Articles

Gauge freedom in chiral gauge theory with vacuum overlap

Dynamical nature of the gauge degrees of freedom and its effect to fermion spectrum are studied at β = ∞ for two- and four-dimensional nonian chiral gauge theories in the vacuum overlap formalism. It is argued that the disordered gauge degrees of freedom does not contradict to the chiral spectrum of lattice fermion.

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open string boundary conditions arise dynamically. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain quark-antiquark static potential from the supergravity side and find that the potential exhibits nonanalyticity of square-root branch cut in `t Hooft coupling parameter. We put forward the nonanalyticity as prediction for large-N gauge theory at strong `t Hooft coupling limit. By turning on Ramond-Ramond zero-form potential, we also study theta-vacuum angle dependence of the static potential. We finally discuss possible dynamical realization of heavy N-prong string junction and of large-N loop equation via local electric field and string recoil thereof. Throughout comparisons of the AdS-CFT correspondence, we find crucial role played by `geometric duality' between UV and IR scales on directions perpendicular to D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.

Spherically symmetric solutions in four-dimensional Poincaré gravity with non-trivial torsion

We study a four-dimensional gauge theory of the Poincaré group with topological action which generalizes some well known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative propagation of excitations around flat spacetime.

The Power of Duality — Exact Results in 4D SUSY Field Theory

Recently the vacuum structure of a large class of four-dimensional (supersymmetric) quantum field theories was determined exactly. These theories exhibit a wide range of interesting new physical phenomena. One of the main new insights is the role of "electric–magnetic duality." In its simplest form it describes the long distance behavior of some strongly coupled, and hence complicated, "electric theories" in terms of weakly coupled "magnetic theories." This understanding sheds new light on confinement and the Higgs mechanism and uncovers new phases of four-dimensional gauge theories. We review these developments and speculate on the outlook.

Type IIA superstrings, chiral symmetry, and N = 1 4D gauge theory dualities

We study N = 1 four-dimensional gauge theories as the world-volume theory of D4-branes between NS 5-branes. We find constructions for a number of known field theory dualities involving SU( N c ) × SU( N′ c ) groups, coupled by matter fields F in the (N c, N − c) representation, in terms of branes of type IIA string theory. The dual gauge group follows from simply reversing the ordering of the NS 5-branes and the D6-branes while conserving magnetic charge on the world-volume of the branes. We interpret many field theory phenomena such as deformation of the superpotential W = Tr (F F ̃ ) k+1 in terms of the position of branes. By looking to D-branes for guidance, we find new N = 1 dualities involving arbitrary numbers of gauge groups. We propose a mechanism for enhanced chiral symmetry in the brane construction which, we conjecture, is associated with tensionless 3-branes in six dimensions.

N = 1 dualities of SO and USp gauge theories and T-duality of string theory

Extending recent work on SO gauge theory, we engineer local string models for N = 1 four-dimensional SO and USp gauge theories coupled to matter in the fundamental. The local models are type IIB orientifolds with D7 branes on a curved orientifold 7-plane, and matter realized by adding D3 branes on the orientifold plane. The Higgs branches of the SO and USp theories can be matched with the moduli spaces of SO and USp instantons on the compact four-dimensional part of the D7 branes world-volume. The R-charge of the gauge theories is identified with a U(1) symmetry on the world-volume of an Euclidean D3 brane instanton. We argue that the quantum field theory dualities of these gauge theories arise from T-dualities of type IIB strings exchanging D7 and D3 charges. A crucial role is played by the induced D3 charge of D7 branes and an orientifold 7-plane, both partially compactified on a Z 2 orbifold of K3.

Exact solutions of exceptional gauge theories from toric geometry

We derive four-dimensional gauge theories with the exceptional groups F 4, E 8, E 7, and E 7 with matter, by starting from the duality between the heterotic string on K3 and F-theory on a elliptically fibered Calabi-Yau 3-fold. This configuration is compactified to four dimensions on a torus, and by employing toric geometry, we compute the type IIB mirrors of the Calabi-Yaus of the type IIA string theory. We identify the Seiberg-Witten curves describing the gauge theories as ALE spaces fibered over a P 1 base.

Black hole solutions in four-dimensional gauge theories of gravity

We study spherically symmetric solutions of a four-dimensional theory of gravity with an action of topological type, which was constructed as a gauge theory of the Poincaré group and can be considered a generalization to higher dimensions of well known two-dimensional models. We also discuss the perturbative degrees of freedom and the properties of the theory under conformal transformations.

Universality of the operator product expansions of SCFT 4

We study the operator product algebra of the supercurrent J α α ̇ and Konishi superfield K in four-dimensional supersymmetric gauge theories. The Konishi superfield appears in the JJ OPE and the algebra is characterized by two central charges c and c′ and an anomalous dimension h for K. In free field (one-loop) approximation, c ∼ 3 N ν + N χ and c′ ∼ N χ , where N ν and N χ are, respectively, the number of vector and chiral multiplets in the theory. In higher order c, c′ and h depend on the gauge and Yukawa couplings and we obtain the two-loop contributions by combining earlier work on c with our own calculations of c′ and h. The major result is that the radiative corrections to the central charges cancel when the one-loop beta-functions vanish, suggesting that c and c′ are invariant under continuous deformations of superconformal theories. The behavior of c and c′ along renormalization group flows is studied from the viewpoint of a c-theorem.

Complex Structures in Quantum Field Theory

We point out that Ward identities imply a notion of reproducing kernel in the set of classical solutions of any quantum field theory, and discuss an application of low-dimensional complex structures in four-dimensional gauge theory.

Anomalous currents in SCFT4

We analyse the critical behaviour of anomalous currents in N=1 four-dimensional supersymmetric gauge theories in the context of electric-magnetic duality. We show that the anomalous dimension of the Konishi superfield is related to the slope of the beta function at the critical point. We construct a duality map for the Konishi current in the minimal SQCD. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of the stress tensor with itself does not close, but mixes with the Konishi operator. As a result in superconformal theories in four dimensions (SCFT$_4$) there are {\sl two} central charges; they allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom. Some applications to N=4 SYM are discussed.

ISOMONODROMIC DEFORMATIONS AND SUPERSYMMETRIC GAUGE THEORIES

Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isospectral problem) too can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of N = 2 SU (s) supersymmetric Yang-Mills theory without matter is considered in detail for illustration. The isomonodromy problem in this case is closely related to the third Painlevé equation and its multicomponent analogs. An implicit relation to [Formula: see text] fusion of topological sigma models is thereby expected.

Gauge-fixing parameter dependence of two-point gauge-variant correlation functions.

The gauge-fixing parameter $\xi$ dependence of two-point gauge variant correlation functions is studied for QED and QCD. We show that, in three Euclidean dimensions, or for four-dimensional thermal gauge theories, the usual procedure of getting a general covariant gauge-fixing term by averaging over a class of covariant gauge-fixing conditions leads to a nontrivial gauge-fixing parameter dependence in gauge variant two-point correlation functions (e.g. fermion propagators). This nontrivial gauge-fixing parameter dependence modifies the large distance behavior of the two-point correlation functions by introducing additional exponentially decaying factors. These factors are the origin of the gauge dependence encountered in some perturbative evaluations of the damping rates and the static chromoelectric screening length in a general covariant gauge. To avoid this modification of the long distance behavior introduced by performing the average over a class of covariant gauge-fixing conditions, one can either choose a vanishing gauge-fixing parameter or apply an unphysical infrared cutoff.

The Power of Duality

Recently the vacuum structure of a large class of four-dimensional (supersymmetric) quantum field was determined exactly. These exhibit a wide range of interesting new physical phenomena. One of the main new insights is the role of electric–magnetic duality. In its simplest form it describes the long distance behavior of some strongly coupled, and hence complicated, electric theories in terms of weakly coupled magnetic This understanding sheds new light on confinement and the Higgs mechanism and uncovers new phases of four-dimensional gauge theories. We review these developments and speculate on the outlook.

Adjoint “quark” color fields in four-dimensional lattice gauge theory: Vacuum screening and penetration

The fields generated by “quarks” in the adjoint representation of SU(2) color are analyzed in the scaling region of the four-dimensional lattice theory. Evidence of vacuum screening of adjoint quarks is obtained from a comparison of quark-antiquark ( Q Q ) flux-tubes for quarks in the adjoint (“isospin” j = 1) and fundamental ( j = 1 2 ) representations. The component ε j of the color-electric field strength in the direction parallel to the Q Q axis is calculated. Near the quarks the ratio of fields ε j=1 ε j= 1 2 approaches the value 8 3 , which is equal to the ratio of SU(2) Casimirs. In between the quarks, the ratio falls well below 8 3 at large R. ε j also falls off rapidly as a function of distance x ⊥ perpendicular to the Q Q axis. However, the ratio ε j=1 ε j= 1 2 depends very weakly on x ⊥. The flux-tubes in the two representations thus appear to have very similar cross-sections. This result could imply that the QCD vacuum is dual to a type I superconductor.

Exact results on the space of vacua of four-dimensional SUSY gauge theories.

We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless particles. Quantum mechanically these singularities can be smoothed out. Alternatively, new massless states appear there. These may be the elementary massless particles or new massless bound states.

Functional integrals for abelian anomalous gauge theories

The functional integral for a four-dimensional abelian anomalous gauge theory is constructed by taking constraints and anomalies into account. It is found to differ from the naïve Lagrangian form. A gauge invariant reformulation is possible, provided (gauge-) covariant anomalies are used. In both formulations, Lorentz invariance seems to be violated. The twodimensional chiral Schwinger model, if treated in the same way, leads to the familiar gauge invariant formulation which is Lorentz invariant.

Gauge anomalies in an effective field theory

A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff Λ, beyond which the locality of the theory breaks down. The maximal Λ can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.

Three-dimensional QED at finite temperature

We investigate the finite temperature behaviour of (2+1)-dimensional QED with N flavours of fermions. The Landau gauge photon propagator is calculated to leading order in the large- N expansion at zero frequency. As in four-dimensional gauge theories the temporal component of the photon acquires a mass at non-zero temperature and static external electric fields are screened. We study the effect of thermal screening on dynamical fermion mass generation using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy. Numerical results for the temperature dependence of the dynamically generated fermion mass are presented for a range of values of the gauge coupling and of N. We find a non-zero critical temperature above which the fermion mass vanishes identically. In particular, we find that the ratio of the zero-temperature fermion mass to the critical temperature is approximately independent of N and is large compared to four-fermion theories.

Cornwall-Norton model in the strong-coupling regime.

The Cornwall-Norton model is studied in the strong-coupling regime. It is shown that the fermionic self-energy at large momenta behaves as X(p)-(m'/p)ln(p/m). We verify that in the strong-coupling phase the dynamically generated masses of gauge and scalar bosons are of the same order, and the essential features of the model remain intact. The Cornwall-Norton model' is one of the simplest models of dynamical gauge-boson-mass generation in four-dimensional gauge theories. In this model the Schwinger-Dyson equation for the fermionic self-energy is quite similar to the one of quantum electrodynamics (QED), and assuming that this equation has a nontrivial solution such as the one proposed for QED by Johnson, Baker, and Willey (JBW), it was shown that the gauge boson acquires a dynamical mass. 3 posteriori, with the use of an efIective potential for composite operators, it was found that the mass generation occurs only when the coupling constant has a moderately small critical value. The model also contains a composite scalar boson, which plays the role of the standard-model Higgs boson and whose mass is numerically small when compared to the gauge-boson mass. Nowadays it is believed that the JBW solution of mass generation in QED is not realized in nature. Maskawa and Nakagima have shown that QED admits a nontrivial solution for the gap equation only when the coupling constant a is larger than a, = — m/3. Further studies confirmed this result, which also imply that even in the presence of a bare mass the nontrivial solution for a (a, disappears when we go to the chiral limit.