Four-dimensional Gauge Theories Research Articles

Perturbative renormalization of null-plane QED.

It has been recognized for some time that quantization on a null plane has several unique and remarkable advantages for the elucidation of quantum field theories. To date these unique features have not been exploited to solve strongly coupled, four-dimensional gauge theories. This is the first in a series of papers aimed at systematically formulating renormalizable gauge theories on the null plane. In order to lay down the groundwork for upcoming nonperturbative studies, it is indispensable to gain control over the perturbative treatment first. A discussion of one-loop renormalization of QED in the Hamiltonian formalism is presented. In this approach, one is faced with severe infrared divergences characteristic of the light-cone gauge. We show how to treat these divergences in a coherent fashion, and thus recover the usual results of the renormalization procedure such as Ward identities and coupling-constant renormalizations.

Constraint structure and quantum equations of motion of anomalous chiral gauge theories in four dimensions.

Using a method proposed recently and checked in the two-dimensional case we calculate the constraint structure and the quantum equations of motion in four-dimensional chiral gauge theories. We arrive at the ordinary Maxwell equations by a remarkable cancellation of anomalous contributions. Furthermore, Fujikawa's relation is found to hold, which requires the vanishing of the current anomaly to be a constraint.

A Kähler-Chern-Simons theory and quantization of instanton moduli spaces

A five-dimensional field theory is introduced which is an analogue of three-dimensional Chern-Simons theory. The reduced phase space in the theory is a moduli space of instantons in four-dimensional euclidean gauge theory, with a symplectic structure induced by the Donaldson μ-map. Issues related to quantization are discussed.

Lorentz non-covariance of lattice chiral gauge theories

We show that, in the continuum limit, the four-dimensional chiral gauge theory built from Wilson fermions with radially frozen Higgs fields leads to Lorentz non-covariant terms in the vacuum polarization tensor, despite the gauge invariance of the regularization. The computation is done when n f, the number of flavors, is large.

Self-dual models with theta terms

There exists a large class of models which are self-dual with respect to inversion of coupling constants. When a theta term is added, this duality may be extended to an invariance under an action of an infinite discrete modular group on the coupling parameter space. In particular, four-dimensional abelian lattice gauge theories possess a Sp(2k, Z) modular symmetry, where k is the number of simple factors in the gauge group. We generalize this result to models of arbitrary dimension, and show that the partition functions of two-dimensional Z N spin models with 2 k flavors and string compactifications on k-dimensional tori are invariant under O(k, k; Z) . We also draw some suggestive parallels to the fractional quantum Hall effect.

Non-Abelian gauge theories with Weyl fermions: The stochastic quantization approach.

We apply the stochastic quantization method to the analysis of the non-Abelian anomaly in a four-dimensional gauge theory coupled to Weyl fermions. We develop a method which leads in a very simple way both to the covariant and the consistent anomaly.

Wilson flux breaking and coset space dimensional reduction

Higher dimensional gauge theories lead, after dimensional reduction on coset spaces, to four-dimensional gauge theories usually with the natural emergence of a Higgs sector which is completely determined. However, the Higgs fields never appear in the adjoint representation which in many GUTs could lead to a successful spontaneous symmetry breaking towards the low energy gauge group. As an alternative we suggest that the breaking of the four-dimensional GUTs obtained from CSDR could be provided by the Wilson flux breaking and we discuss some semirealistic examples. We also speculate on the possibility that the breaking of the electroweak sector has dynamical origin.

Geometrical hierarchy and spontaneous symmetry breaking

A four-dimensional gauge theory, where Higgs fields and the corresponding potential appear naturally, is obtained by dimensionally reducing a pure gauge theory over a compact coset space S R . We show, using an explicit example, that a hierarchy of the scales in the coset space can change the spontaneous symmetry breaking of the four-dimensional gauge theory.

Topology of gauge theories on compact 4-manifolds

In a gauge theory the topological structure of the group of gauge transformations G can have important consequences. Information is obtained about the topology of G in four dimensions and this is used to study the existence of a global gauge fixing condition. The topologies nature of G also allows inequivalent topological sectors to exist and these are discussed in four- and five-dimensional gauge theories. Finally, the topological structure of G imposes constraints on the existence of global anomalies in four-dimensional gauge theories.

On four-dimensional gauge theories from type II superstrings

We study the four-dimensional gauge theories which are associated with classical vacua of the type II superstring, i.e. which correspond to a superconformal field theory on the world sheet. Using the fact that gauge symmetry arises from a supersymmetric affine Kac-Moody algebra, and demanding unitarity of the underlying world-sheet field theory, we show that no such vacua can yield the particle spectrum of the standard model. Of the gauge theories which are permitted by unitarity, we find that many can be constructed explicitly as orbifolds which twist the left- and right-moving degrees of freedom of the string asymmetrically; among these are three N = 4 supersymmetric models - which have previously been constructed in a quite different fashion - and two N = 1 supersymmetric models with chiral gauge representations for the massless fermions.

Monte Carlo analysis of the 2D chiral SU(2) × SU(2) lattice theory with a spin- [formula omitted]action

Using Monte Carlo simulations, the phase structure of the two-dimensional SU(2)×SU(2) lattice theory with an action defined through the spin- 3 2 representation of the SU(2) matrices has been determined. A second-order phase transitions has been found, like the SO(3)×SO(3) chiral model, in contrast to the equivalent four-dimensional lattice gauge theory with the 3 2 representation action that exhibits a clear first-order transition.

Chiral anomalies, nonminimal couplings, and Kaluza-Klein theory.

By making use of the heat kernel, the chiral anomalies for two- and four-dimensional Abelian gauge theories with Pauli couplings (such as Kaluza-Klein higher-dimensional models) are derived. These are reduced to the minimal anomalies after adding counterterms to the action and by redefining the axial-vector current; confirmation of these counterterms is provided by diagrammatic analysis. Summing over the fermion modes, both the counterterms and the anomalies disappear.

Instanton- and monopole-induced compactification ofCP N space and chiral fermions in the Einstein-Yang-Mills theory

We study the Einstein-Yang-Mills theory which has a classical solution of instanton-monopole configuration on an internalCPN space and leads to a four-dimensional effective gauge theory with an isometry groupSUN+1. We derive the generalized Dirac quantization condition in the presence of instanton monopole, so that the fermion is well accommodated in the isotropy group with a nontrivial representation associated with an instanton monopole. After harmonic expansions, we look for a chirally isolated fermion representation and derive a theorem to obtain a massless fermion. Several examples which satisfy the anomaly-free condition are studied. It is shown thatSO14 andSO18 gauge theories give spectra of generation numbers, 1, 3, 7, … and 1, 5, … of16L inSO10, respectively. We also study examples fromE8⊗E8 superstring theory.

Mean-field approximation for Abelian and non-Abelian lattice gauge theories at finite temperature.

The phase diagrams of the Z(2), Z(3), and SU(2) four-dimensional lattice gauge theories at finite temperature are analyzed by the mean-field technique including Gaussian corrections. The effect of the finite size of the lattice in the time Euclidean direction is considered at lowest order by the Bethe-Peierls approximation. We discuss the gauge dependence of the results. The predictions for Abelian models are excellent but for SU(2) we show that in order to reproduce the Monte Carlo--simulations results, the Gaussian corrections are not enough and higher-loop calculations may be necessary.

Energy and angular-momentum non-conservation in four-dimensional gauge theories

We study energy and angular-momentum non-conservation in four-dimensional chiral gauge theories using Landau levels. These effects are physical manifestations of the usual gauge anomaly, and enable us to understand in a semi-classical approximation why anomaly cancellation is required for a consistent field theory.

A theoretical and numerical analysis of disorder operators in the chiral models

Abstract We analyze disorder operators in the chiral models in order to better understand the behavior of 't Hooft loops in four-dimensional gauge theories. We use both theoretical and numerical approaches.

Topology of 2D lattice gauge fields

A local topological charge density for two-dimensional (2d) U(1) lattice gauge field is defined. A Monte Carlo (MC) simulation of pure 2d U(1) lattice gauge theory is carried out and results are obtained for the topological susceptibility and the mean value of the topological charge density in units of the string tension in a θ vacuum. The dilute gas approximation appears to be very successful. Definitions of the topological charge not based on a local charge density, analogous to the ones used in MC studies of four-dimensional lattice gauge theories, are also considered and detailed comparisons are made. These non-local charges are found to have several undesirable features.

Effective transfer matrix for low-lying glueball states in lattice gauge theory

In four-dimensional lattice gauge theory without quarks the lowest particle states in the strong coupling region correspond to a spin-zero and a spin-two glueball. They are degenerate in the lowest order of the strong coupling expansion. There exists an effective transfer matrix, acting in the lowest order eigenspace, whose eigenvalues are identical with the corresponding ones of the full transfer matrix to all orders in the strong coupling expansion. It is constructed here up to the eighth nontrivial order for different gauge groups. Diagonalization yields the energy-momentum dispersion relations for glueball states.

Fermion mass predictions from higher dimensions

Higher dimensional theories predict ratios between Yukawa couplings and gauge couplings in the resulting four-dimensional gauge theory. After spontaneous symmetry breaking of weak interactions, these relations are converted into relations between particle masses. We calculate explicitly the Yukawa couplings resulting from a six-dimensional SO(12) gauge theory. We argue that the fermion masses follow the pattern m t, ≫ m b, m c m τ ≫ m s, m μ ≫ m d, m u, m e.

Chiral condensate with Wilson fermions

We show that for Wilson fermions on the lattice the continuum contribution to 〈 ψ ψ〉 can be unambiguously separated form the perturbative tail which arises because of the explicit chiral symmetry breaking. This phenomenon is shown to happen in the Gross-Neveu model to order 1 N , and we give general arguments for the occurrence of the same situation in four-dimensional gauge theories.