The Condensate for SU(2) Yang-Mills Theory in 1+1 Dimensions Coupled to Massless Adjoint Fermions

TL;DR

This paper analyzes SU(2) Yang-Mills theory in 1+1 dimensions with massless adjoint fermions, revealing a nontrivial vacuum structure and condensate effects using light-front quantization.

Contribution

It provides exact vacuum state expressions and constructs the ta vacuum in a 1+1D SU(2) gauge theory with adjoint fermions, highlighting topological features.

Findings

Identification of two topological sectors and ta vacuum structure

Exact expressions for vacuum states in light-front quantization

Condensate influences string tension in massive theory

Abstract

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a \theta vacuum. We show how this feature is realized in light-front quantization, using discretization of x^- as an infrared regulator. We find exact expressions for the vacuum states and construct the analog of the \theta vacuum. We calculate the bilinear condensate of the model. We argue that this condensate does not effect the spectrum of the massless theory but gives the string tenson of the massive theory.