Reducible gauge algebra of BRST-invariant constraints

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anti-commuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.     

Topology of the gauge condition and new confinement phases in non-abelian gauge theories

The gauge-fixing constraint in a gauge field theory is crucial for understanding both short-distance and long-distance behavior of non-abelian gauge field theories. We define what we call “non-propagating” gauge conditions such as the unitary gauge and “approximately non-propagating” or renormalizable gauge conditions, and study their topological properties. By first fixing the non-abelian part of the gauge ambiguity we find that SU(N) gauge theories can be written in the form of abelian gauge theories with N ? 1 fold multiplicity enriched with magnetic monopoles with certain magnetic charge combinations. Their electric chargesare governed by the instanton angle θ.If θ is continuously varied from 0 to 2π and a confinement mode is assumed for some θ, then at least one phase-transition must occur. We speculate on the possibility of new phases: e.g., “oblique confinement,” where $\text{θ ? π}$, and explain some peculiar features of this mode. In principle there may be infinitely many such modes, all separated by phase transition boundaries.     

Local and global gauge symmetries in temporal gauge

In the temporal gauge formalism, in order to make a distinction between the global limit of local gauge transformations and global ones a non-local operator, θ, is introduced. It is claimed that what kind of θ is used is equivalent to what kind of gauge-fixing schemes is chosen. Along this idea, in non-abelian theories the coulomb, axial and unitary gauges have been investigated. In the unitary gauge spontaneous breakdown of global gauge symmetry has been found to be reduced to a problem of the boundary condition for the Higgs field and the occurrence of symmetry breaking has been concluded.     

Rigid symmetries and BRST-invariance in gauge theories

The structure of the symmetry algebra of theories with simultaneous local and rigid symmetries is analyzed. BRST-invariant Faddeev-Popov gauge-fixing in such theories is discussed and it is proven that the BRST-transformations can always be made to commute with the rigid symmetries by assigning specific transformation rules to the ghosts. The problem of keeping the rigid symmetries manifest in the quantum theory is shown to reduce to the problem of finding covariant gauge conditions. Such covariant gauges exist only if the algebra of local and rigid symmetries has a semi-direct product structure.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.     

String field theory in the Siegel gauge

We specialize the gauge-fixing procedure for the Witten action of the open bosonic string, given in a preceding paper, choosing the Siegel gauge. We find that the BRST-invariant gauge-fixed action is the gauge invariant one with ghost number unrestricted plus a gauge-fixing term. The BRST invariance of the measure in the functional integral is briefly discussed. As a technical tool the Hodge dual of a string functional is defined.     

Explicit two-loop calculation of decoupling in unbroken gauge theories with fermions

Unbroken gauge theories containing light as well as heavy fermions are considered in the limit of the mass of the heavy fermions tending to infinity. The effective coupling constant of the decoupled low-energy theory thus obtained, has been calculated up to two-loop level using the light particle irreducible vertex function and the background field formalism. In addition, to simplify the computation, a background field gauge-fixing term has been used, because in such a gauge the effective coupling constant can be calculated from a two-point function only. Our analysis reveals that in the non-abelian theory, the simple algorithm proposed by Ovrut and Schnitzer for computing the effective coupling constant up to the two-loop level is valid only in the α = 0 or α = ?3 background field gauge. A general procedure correct for all values of α is described.     

Gauge fixing for gravity-coupled theories and the super-Higgs effect beyond the unitary gauge

A straightforward gauge-fixing procedure is presented for a general gauge theory coupled to gravity, which relies on the geometrical nature of the BRS symmetry. It promotes the Stueckelberg “auxiliary” field (and its generalizations) to the level of a fundamental quantum field, like ghosts and antighosts. In this way, the Nielsen-Kallosh phenomenon is fully clarified, and a complete derivation of the quantum lagrangian of N = 1, D = 4 “new minimal” supergravity is given. As an output we analyze the super-Higgs effect beyond the unitary gauge and find a particularly simple gauge analogous to the 't Hooft-Feynman one for spontaneously broken Yang-Mills theories.     

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.     

Comment on real-time finite-temperature gauge field propagators

The gauge-fixing terms of the free, real-time thermal gauge field propagators corresponding to quantization in a covariant gauge obtained by Kobes, Semenoff, and Weiss are shown to be incorrect, apart from well-known signature ambiguities in the off-diagonal elements, and to differ from those obtained by Landsman using the method of the Klein-Gordon divisor. We obtain the correct forms which are then shown to coincide with Landsman's results by means of a distributional identity.     

On the gauge independence of the S-matrix

The S-matrix is invariant with respect to the variation of any (global) parameter involved in the gauge-fixing conditions, if that variation is accompanied by a certain redefinition of the basis of polarization vectors. Renormalizability of the underlying gauge theory is not required. The proof is nonperturbative and, using the “extended” BRS transformation, quite simple. Received: 27 April 2001 / Published online: 6 July 2001     

Spontaneous symmetry breaking of Slavnov symmetry A restriction on the gauge condition

It is shown that the condition of vanishing vacuum expectation value of the gauge operator, using a gauge-fixing term quadratic in this operator, does not necessarily follow from the Slavnov identity, due to a possible spontaneous breakdown of the Slavnov symmetry. For a consistent renormalization such a condition may have to be imposed order by order in perturbation theory, depending on the choice of the gauge. This restriction on non-singular gauges is particularly relevant for the discussion of the spontaneously broken realizations of the gauge symmetry.     

Manifestly-covariant canonical formalism of Poincaré gauge theories

We present a general framework for manifestly-covariant canonical formulation of Poincaré gauge theories. We construct a general class of action that is invariant under two kinds of BRS transformations—translation and internal Lorentz—and suitable for manifestly-covariant canonical quantization. This theory contains a great number of conserved quantities, which we investigate systematically. It is also pointed out that a canonical formulation of higher-derivative theories may be obtained as a limiting case in this framework.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Finite BRST Mapping in Higher-Derivative Models

We continue the study of finite field-dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which incudes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.     

Cold atoms in non-Abelian gauge potentials: from the Hofstadter "moth" to lattice gauge theory

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.     

Gauge dependence of ultraviolet behavior of gauge theories

The gauge dependence of ultraviolet behavior of gauge theories is examined on the basis of renormalization-group equation. Non-Abelian gauge theories are confirmed to be asymptotically free in an arbitrary gauge. It is also shown that the effective gauge parameter approaches a finite value in the ultraviolet limit in contrast with the case of QED.     

Complexification of gauge theories

For the case of a first-class constrained system with equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations G is equivalent to the single process of dividing out the initial phase space by the complexification G_C of G. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold for the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.