BRST Cohomology and Vacuum Structure of Two-Dimensional Chromodynamics

TL;DR

This paper explores the vacuum structure of two-dimensional QCD using BRST cohomology, revealing a finite set of vacua and their degeneracy for the SU(2) gauge group, within a conformal field theory framework.

Contribution

It introduces a novel approach to analyze QCD_2 by relating BRST conditions to a G/G topological theory and solving the cohomology problem to identify vacua.

Findings

Finite set of vacua identified for G=SU(2)

Vacua exhibit two-fold degeneracy for SU(2)

BRST conditions restrict the conformally invariant sector

Abstract

Using a formulation of QCD_2 as a perturbed conformally invariant theory involving fermions, ghosts, as well as positive and negative level Wess-Zumino-Witten fields, we show that the BRST conditions become restrictions on the conformally invariant sector, as described by a G/G topological theory. By solving the corresponding cohomology problem we are led to a finite set of vacua. For G=SU(2) these vacua are two-fold degenerate.