BRST Approach Research Articles

AUXILIARY REPRESENTATIONS OF LIE ALGEBRAS AND THE BRST CONSTRUCTIONS

The method of constructing auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be non-hermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proven for any Lie algebra.

A general BRST approach to string theories with zeta function regularizations

We propose a new general BRST approach to string and string-like theories that have a wider range of applicability than, e.g., the conventional conformal field theory method. The method involves a simple general regularization of all basic commutators, which makes all divergent sums expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particularly useful in order to investigate possible state space representations to a given model. The method is applied to three string models: The ordinary bosonic string, the tensionless string, and the conformal tensionless string. We also investigate different state spaces for these models. The tensionless string models are treated in detail. Although we mostly rederive known results, they appear in a new fashion that deepens our understanding of these models. Furthermore, we believe that our treatment is more rigorous than most of the previous ones. In the case of the conformal tensionless string we find a new solution for d=4.

Irreducible Hamiltonian BRST Approach to Topologically Coupled Abelian Forms

An irreducible Hamiltonian BRST approach to topologically coupled p- and (p + 1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST point of view to the original redundant theory. The irreducible path integral can be brought to a manifestly Lorentz covariant form.

DESCRIPTION OF THE HIGHER MASSLESS IRREDUCIBLE INTEGER SPINS IN THE BRST APPROACH

The BRST approach is applied to describe the irreducible massless higher spins representation of the Poincaré group in arbitrary dimensions. The total system of constraints in such theory includes both first- and second-class constraints. The corresponding nil-potent BRST charge contains terms up to the seventh degree in ghosts.

The Semi-Infinite Cohomology of Affine Lie Algebras

We study in detail the semi-infinite or BRST cohomology of general affine Lie algebras. This cohomology is relevant in the BRST approach to gauged WZNW models. We prove the existence of an infinite sequence of elements in the cohomology for non-zero ghost numbers. This will imply that the BRST approach to topological WZNW model admits many more states than a conventional coset construction. This conclusion also applies to some non-topological models. Our work will also contain results on the structure of Verma modules over affine Lie algebras. In particular, we generalize the results of Verma and Bernstein-Gel'fand-Gel'fand,for finite dimensional Lie algebras, on the structure and multiplicities of Verma modules.

Dimensional Reduction and BRST Approach to the Description of a Regge Trajectory

The local free field theory for Regge trajectory is described in the framework of BRST quantization method. The corresponding BRST charge is constructed using the method of dimensional reduction.

FIELD-ANTIFIELD QUANTIZATION OF THE YANG-MILLS THEORY WITH EXTENDED BRST INVARIANCE IN THE COLLECTIVE FIELD APPROACH

The collective field procedure is an interesting way of deriving the field-antifield formalism from a standard BRST approach. Trivial shift symmetries are introduced in the original gauge theory and then a judicious choice of gauge-fixing leads to the identification of the antighosts of these extra symmetries as the antifields. When explicit extended BRST invariance (BRST and anti-BRST invariance) is required, two collective fields are necessary, and the gauge-fixing structure is more complex. In this article, with the purpose of clarifying some aspects of this procedure, we consider in detail the example of the Yang–Mills theory.

Gauged supersymmetric WZNW model using the BRST approach

We consider the supersymmetric WZNW model gauged in a manifestly supersymmetric way. We find the BRST charge and the necessary condition for nilpotency. In the BRST framework the model proves to be a Lagrangian formulation of the supersymmetric coset construction, know as the N = 1 Kazama-Suzuki coset construction.

Perturbative calculations in the effective lagrangian and 2d closed string field theory

This paper is devoted to the study of closed string field theory in two dimensions. We compare two different approaches: BRST closed string field theory and the string effective Lagrangian. We show that the quadratic actions and the pole structures of tree-level scattering amplitudes agree. We study merits and drawbacks of various gauge fixing procedures. In particular, we discuss the conformal gauge in the context of the effective Lagrangian, and Siegel and Lorentz-like gauge in the general BRST approach. We discuss the ways in which discrete states survive a particular gauge fixing both by directly solving the equations of motion, and by analyzing the pole structure of the scattering amplitudes.

The BRST formulation of G/H WZNW models

We consider a BRST approach to G/H coset WZNW models, i.e. a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the BRST cohomology. This will reveal a remarkable connection between integrable representations and a class of non-integrable representations for negative levels. The latter representations are also connected to string theories based on non-compact WZNW models. The partition functions of G/H cosets are also considered. The BRST approach enables a covariant construction of these, which does not rely on the decomposition of G as G/H × H. We show that for the well-studied examples of SU (2) k × SU (2) 1/SU (2) k+1 and SU (2) k /U (1), we exactly reproduce the previously known results.

BRST approach to translational symmetry and the geometry of flat manifolds with torsion

A BRST treatment of translational symmetry on flat manifolds, where torsion does not vanish, displays well-known features of differential geometry. In particular the covariant exterior derivative operator is identified as the BRST operator corresponding to translational symmetry. Its nilpotency is due to vanishing curvature on the manifold.

Relativistic framework for soliton quantization

We describe a method for the quantization of solitons moving with arbitrary momentum based on the BRST approach. We show that the treatment naturally leads to expressions satisfying Lorentz invariance. As an application of this procedure we evaluate the one and two loop corrections to the soliton energy.

A new approach to BRST operator cohomologies: Exact results for the BRST-fock theories

The modification of the BRST approach suggested by the authors and based on using the Lie superalgebra l(1, 1) as the full algebra of the BRST symmetry is applied to the problem of calculating BRST operator cohomologies. The calculation is done for the class of BRST-Fock theories. The operator cohomologies are proved to be trivial. The result is interpreted as the analog of the no-ghost theorem on the level of observables.

POLYMERS AND TOPOLOGICAL FIELD THEORY

We show that the generating function for self-avoiding paths is formally obtainable from a Witten topological field theory, even if the physical quantities for polymers are not the physical quantities in the BRST approach. We argue that in the dense phase the BRST invariance should generally be broken at the quantum level.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GRAVITY IN THE LIGHT-CONE GAUGE

The BRST approach to two-dimensional gravity coupled to conformal field theories is discussed. The ordinary BRST symmetry acts only on the left-moving sector of the theory. It is found that there exists a BRST-like symmetry also in the right-moving sector. The conserved charge of this new symmetry is found to be nilpotent. This symmetry is a result of a redundancy of the parametrization of the gravitational field in terms of a scalar field. We propose that the physical states of the theory should belong to the cohomology of this BRST-like charge to eliminate the redundancy. It is also discussed how to derive the BRST charge from the action and the transformation laws of fields.

Improved covariant quantization of the heterotic superstring

A generalized lagrangian BRST formalism is developed and used to study the covariant quantization of the heterotic superstring. The quantum action is by construction invariant under the off-shell nilpotent BRST transformations, which is achieved by introducing a minimal set of auxiliary variables with nonzero ghost number. The method relies on the classical gauge structure, and represents a natural lagrangian extension of the ideas existing in the hamiltonian BRST approach.

BOUNDARY CONDITIONS IN FIRST QUANTIZATION

In the BRST approach to first quantization, bosonic ghosts can cause ambiguities in the cohomology (and thus in second quantization). We show how nonminimal terms give a general solution to this problem, avoiding the need for “picture-changing operators.” As examples, we consider spinning particles, superparticles, covariantized light cone bosonic string field theory, and NSR superstring field theory.

THE INFINITELY REDUCIBLE GAUGE SYMMETRY IN UNCONSTRAINED BRST YANG-MILLS THEORY

A study is made of the infinitely reducible prepotential gauge symmetry recently found in the unconstrained BRST approach to Yang-Mills theory. This symmetry has an associated set of “BRST for BRST” transformations. The unconstrained BRST approach is applied to these, and constraints upon the field strengths of suitable gauge fields are shown to yield the BRST for BRST rules. The unconstrained BRST approach in fact applies ad infinitum, and we give the general form of the gauge-invariant Yang-Mills action in terms of appropriate prepotentials.

BRST cohomology and BRST gauge fixing

We discuss some general aspects of BRST cohomology. We investigate the BRST gauge-fixing procedure based on the harmonic gauges in the ghost-extended quantum mechanical Hilbert space. We obtain a general classification of states according to their BRST transformation properties. On the basis of these results we find necessary and sufficient conditions for the positivity of the physical state space and establish their equivalence with another set of conditions introduced by Spiegelglas. We apply the method to a system with a non-semisimple, solvable algebra of first-class constraints, which appears in the theory of massless higher spins. We find that both the Dirac and Gupta-Bleuler quantization procedures are contained within the BRST approach, but they correspond to different cohomology classes.

On the abelization theorem in the BRST approach

The abelization theorem is proved on the quantum level in the framework of perturbation theory. An application of the theorem to the problem of the positivity of the physical subspace norm is considered.