Nonperturbative Effects from Perturbation Theory in Adjoint QCD_{1+1}

TL;DR

This paper investigates the nonperturbative vacuum structure and fermion condensate in adjoint SU(2) gauge theory in 1+1 dimensions, using a specialized quantization approach to facilitate perturbative calculations.

Contribution

It introduces a consistent quantization scheme for adjoint QCD in 1+1 dimensions that handles unphysical gauge modes and enables perturbative analysis of the vacuum and condensate.

Findings

Vacuum evaluated to second order in perturbation theory.

Fermion condensate estimated using perturbative vacuum.

Quantization scheme ensures residual gauge symmetry is preserved.

Abstract

SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions, periodic for one colour component (the diagonal 3- component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-colour component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.