Hamiltonian, Path Integral and BRST Formulations of Large N Scalar $QCD_{2}$ on the Light-Front and Spontaneous Symmetry Breaking

TL;DR

This paper explores the Hamiltonian, path integral, and BRST formulations of large-N scalar QCD in 2D on the light-front, focusing on spontaneous symmetry breaking with a Higgs potential, ensuring gauge invariance and analyzing constraints.

Contribution

It introduces the light-front Hamiltonian, path integral, and BRST formulations of large-N scalar QCD with a Higgs potential, highlighting spontaneous symmetry breaking in these frameworks.

Findings

Gauge invariance of the light-front theory confirmed

Explicit spontaneous symmetry breaking demonstrated in different gauges

First-class constraints identified in the gauge-invariant formulation

Abstract

Recently Grinstein, Jora, and Polosa have studied a theory of large-$N$ scalar quantum chromodynamics in one-space one-time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of $SU(N)$ and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge-invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge.