Adjoint $QCD_{1+1}$ in Light-cone Gauge, Quantized at Equal Time

TL;DR

This paper studies SU(2) adjoint QCD in 1+1 dimensions using light-cone gauge, focusing on vacuum structure and fermion condensate, and introduces a consistent quantization scheme for gauge fields with implications for perturbative analysis.

Contribution

It develops a consistent quantization method for gauge fields in adjoint QCD in 1+1 dimensions, addressing issues with indefinite metrics and residual gauge symmetry.

Findings

Proper quantization of unphysical gauge modes is essential for consistency.

Vacuum structure analyzed up to second order in perturbation theory.

Approximate fermion condensate value obtained from perturbative vacuum.

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 color 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-color 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.