Extended QCD(2) from dimensional projection of QCD(4)

TL;DR

This paper derives an extended (1+1)-dimensional QCD model from 4D QCD via dimensional reduction, revealing dynamical mass generation, chiral symmetry breaking, and properties of bound states, including a generalized 't Hooft pion.

Contribution

It introduces a new extended QCD(2) model from 4D QCD, analyzing dynamical phenomena and bound states within a large N_c, light cone gauge framework.

Findings

Dynamical mass generation for transverse gluons.

Chiral symmetry breaking with non-tachyonic quark masses.

Existence of a massless pseudoscalar ground state.

Abstract

We study an extended QCD model in (1+1) dimensions obtained from QCD in 4D by compactifying two spatial dimensions and projecting onto the zero-mode subspace. We work out this model in the large $N_c$ limit and using light cone gauge but keeping the equal-time quantization. This system is found to induce a dynamical mass for transverse gluons -- adjoint scalars in QCD(2), and to undergo a chiral symmetry breaking with the full quark propagators yielding non-tachyonic, dynamical quark masses, even in the chiral limit. We study quark-antiquark bound states which can be classified in this model by their properties under Lorentz transformations inherited from 4D. The scalar and pseudoscalar sectors of the theory are examined and in the chiral limit a massless ground state for pseudoscalars is revealed with a wave function generalizing the so called 't Hooft pion solution.