Massive Yang-Mills Theory Research Articles

Differential regularization of topologically massive Yang-Mills theory and Chern-Simons theory

We apply a differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of a three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive Yang-Mills theory. We then consider Chern-Simons field theory as the large mass limit of topologically massive Yang-Mills theory and show that this leads to the famous shift in the parameter $k$. Some useful formulas for the calculus of differential renormalization of three-dimensional field theories are given in an Appendix.

Extravariables in the BRST quantization of second-class constrained systems. Existence theorems

In this paper we show how the BRST quantization can be applied to systems possessing only second-class constraints through their conversion to some first-class ones starting with our method exposed in a previous paper [Nucl. Phys. B 456 (1995) 473]. Thus, it is proved that (i) for a certain class of second-class systems there exists a standard coupling between the variables of the original phase space and some extravariables such that we can transform the original system into a one-parameter family of first-class systems; (ii) the BRST quantization of this family in a standard gauge leads to the same path integral as that of the original system. The analysis is accomplished in both reducible and irreducible cases. At the same time, the Lagrangian action of the first-class family is obtained and its provenance is clarified. In this context, the Wess-Zumino action is also derived. The results from the theoretical part of the paper are exemplified in detail for the massive Yang-Mills theory and for massive abelian three-form gauge fields.

The Higgs — an infrared companion of massive Yang-Mills theory

From the fact that massive Yang-Mills theory can be rewritten as a gauge invariant nonlinear σ-model we derive in a large N limit ( N = 4 in the S.M.) the parameters of the S.M. Higgs sector which appears below a typical momentum scale of order 1.2 TeV. The Higgs mass becomes m H = 3v ≌ 426 GeV . The symmetry breaking effect of the large top mass plays a major role in our formalism.

The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory

In this paper, we complete our study of one-loop perturbative Chern-Simons theory in the light-cone gauge n· A a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function Λ μνω abc ( p 1, p 2, p 3) to one loop. The spurious poles of ( q· n) −1 in the gauge propagator are treated with the n μ ∗- prescription . It is shown that the vertex function, which contains both local and nonlocal terms, is UV finite, respects the Ward identity and agrees with the one-loop effective action proposed in the preceding paper.

Non-gauge fixing approach to chiral gauge theories using staggered fermions

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the gauge non-invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory. This scenario is very attractive since it does not rely on gauge fixing. We investigate a simple realization of this approach in a U(1) axial-vector model with dynamical fermions in four dimensions. A detailed numerical exploration of the phase diagram of this model on small lattices gives us no indication that the desired gauge symmetry restoration takes place. Since simulation of the model on larger lattices leads to severe numerical problems, we conclude that this simple realization of the non-gauge fixing approach has failed, at least in practice.

Physically meaningful and not so meaningful symmetries in Chern-Simons theory

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action that is both Becchi-Rouet-Stora (BRS) invariant and Landau supersymmetric and an effective action that is only BRS invariant is a finite field redefinition. Having established this, we use a BRS-invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift $k\ensuremath{\rightarrow}k+{c}_{V}$ of the bare Chern-Simons parameter $k$ in connection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS-invariant regulators used as yet yield the same value for the shift.

Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory

We study quantum Chern-Simons theory as the large-mass limit of the limit D→3 of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift k→ k+ c v, k being the bare Chern-Simons parameter. In passing, we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

Hidden sectors with hidden matter

Using previous results on non-perturbative effects in massive supersymmetric Yang-Mills theories, we extend recent considerations on the duality invariant gaugino condensation, within the string effective action approach, to the formation of hidden matter field condensates. The masses of the condensing matter fields are determined by some string background parameters corresponding to vacuum expectation values of additional gauge singlet hidden matter fields. The vacuum degeneracy of these fields is shown to be lifted by non-perturbative condensation effects.

Operator regularization and massive Yang–Mills theory

Operator regularization has proved to be a practical method for computing finite, symmetry preserving Green's functions to arbitrary order in perturbation theory. This finiteness has been shown to persist in such nonrenormalizable theories as [Formula: see text] and quantum gravity; in this paper we apply the technique to massive gauge theories. The mass for the vector particle is inserted by hand using the Stueckleberg–Kunimasa–Goto mechanism; no degree of freedom associated with the Higgs scalar is present in the initial Lagrangian. Several one-loop calculations serve to illustrate that no divergences ever arise in this theory if one uses operator regularization. The one-loop effective action is examined in both 4 and n = (4 − ε) dimensions. The result is finite in 4 dimensions and in (4 − ε) dimensions has the pole structure at ε = 0 found by Kafiev. In four dimensions, we find that, in contrast to the case of renormalizable theories, radiatively induced interactions occur with coefficients depending on log (p2/μ2). Consequently μ2 is no longer an arbitrary parameter but must be fixed experimentally.

Lattice gauge magnets: Local isospin from spin

We study lattice hamiltonians with continuous local SU(2) gauge invariance, for which the Hilbert space on each link is finite dimensional. As these are gauge-invariant generalizations of quantum magnets, we call them lattice gauge magnets. The generators of gauge transformations are built out of local spin operators. In the simplest version of such a theory, the gauge field components belong to a representation of the algebra SO(5). Long-wavelength excitations of this model are gapless and nonrelativistic at the tree level. In 2 + 1 dimensions, we study a parity violating model, which we argue is equivalent to the topologically massive Yang-Mills theory.

Singularity of Green's function and effective action in massive Yang-Mills theories.

The singularities of the one-loop Green's function and the effective action in massive Yang-Mills theory are investigated, in terms of the original (Proca) variables. Although the result is nonrenormalizable, a high degree of predictive power can be maintained.

Gauge invariance and systems with second-class constraints

We show that under a certain assumption systems with second-class constraints can be regarded as gauge-fixed systems with first-class constraints. The massive Yang-Mills theory, a point particle on a sphere and theO(N) symmetric non-linear σ-model are considered as concrete examples.

Hamiltonian methods for nonlinear sigma models

Nonlinear sigma models are studied in n space dimensions with values in a coset space G/H as infinite dimensional Hamiltonian systems. An ‘‘intrinsic’’ formulation is discussed in terms of coordinates on G/H, an ‘‘embedded’’ formulation in terms of fields satisfying a constraint and a ‘‘lifted’’ formulation in terms of fields having values in G/H̄, where H̄ is a normal subgroup of H. The coupling of the sigma model to Yang–Mills fields with structure group G is then considered, and it is shown that this system is equivalent to a massive Yang–Mills theory.

Comment on “Topologically massive gauge theories”

In a recent paper by R. Pisarski and S. Rao concerning topologically massive quantum Yang-Mills theory, the expression of the P-even part of the non-Abelian gauge field selfenergy at one-loop order is shown to obey a consistency condition, which is not fulfilled by the formula originally presented by S. Deser, R. Jackiw, and S. Templeton. In this comment, I present a recalculation which agrees with Pisarski and Rao.

MASSIVE YANG-MILLS THEORY: RENORMALIZABILITY VERSUS UNITARITY

Various massive Yang-Mills theories not based on the Higgs mechanism are investigated. They are subject to conflicting demands in the twin requirements of unitarity and perturbative renormalizability. Either one or other of these requirements is violated. Unitarity is considered in some detail.

Hamiltonian analysis of topologically massive Yang-Mills theory.

The Hamiltonian dynamics of three-dimensional topologically massive Yang-Mills theory is analyzed in both normal and null-plane coordinates using Dirac's constraint formalism. As expected, the physical degrees of freedom correspond to a single self-interacting massive mode. In null-plane coordinates, we obtain the standard result that the number of canonical degrees of freedom is half the number found using a spacelike initial-value surface.

Renormalization schemes and renormalization group functions in Yang–Mills theories with massive fermions

The connection between renormalization schemes (RS’s) and the renormalization group (RG) functions for a massive Yang–Mills theory is investigated. The RS’s are defined in a manner independent of the regularization procedure. The RS transformations are defined in such a way that it is clear that they form a group. It is shown that to a given set of RG functions corresponds an infinite number of RS’s. The subgroup of RS transformations which leave invariant the (mass-shell) MS-RG functions is carefully described. Gauge invariance, regularity of the theory when m→0 and mass decoupling are imposed and the corresponding indeterminations of RS’s are given. It is seen that a RS which fulfills simultaneously the above conditions does not exist.

Hidden local symmetry versus massive Yang-Mills theory in the nonlinear chiral Lagrangian.

Based on the generalized hidden local symmetry in the chiral nonlinear \ensuremath{\sigma} model, I present a unified description of the \ensuremath{\pi}, \ensuremath{\rho}, and ${A}_{1}$ mesons coupled to the gauge bosons of the Glashow-Salam-Weinberg model, which relates various approaches including the old massive Yang-Mills Lagrangian.

Spin and statistics in topologically massive Yang-Mills theories

Topologically massive Yang-Mills therries are shown to lack a fermionic sector of quantum states similar to that of non-linear sigma models with a Wess-Zumino term in the lagrangian. The result is based on the topological triviality of the orbits of the rotation group in the space of gauge orbits M , and is not related to the absence of classical solitons.