Light-Front QCD(1+1) Coupled to Chiral Adjoint Fermions

TL;DR

This paper explores the vacuum structure and topological features of SU(N) gauge theory in 1+1 dimensions coupled to chiral adjoint fermions, revealing exact vacuum states and condensates using light-front quantization.

Contribution

It provides a detailed analysis of the nontrivial vacuum topology and heta vacuum structure in light-front quantized SU(N) gauge theory with chiral adjoint fermions, including exact solutions for vacuum states.

Findings

Exact expressions for degenerate vacuum states

Identification of heta vacuum in light-front quantization

Calculation of fermion condensate

Abstract

We consider SU(N) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually SU(N)/Z_N, which possesses nontrivial topology. In particular, there are N 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 for the case N=2, using discretization as an infrared regulator. In the discretized form of the theory the nontrivial vacuum structure is associated with the zero momentum mode of the gauge field A^+. We find exact expressions for the degenerate vacuum states and the analog of the \theta vacuum. The model also possess a condensate which we calculate. We discuss the difference between this chiral light-front theory and the theories that have previously been considered in the equal-time approach.