Functional renormalization of QCD in $1 + 1$ dimensions: four-fermion interactions from quark-gluon dynamics

TL;DR

This paper applies the Functional Renormalization Group to 2D QCD, deriving flow equations for key parameters and revealing the theory's behavior from ultraviolet to infrared, setting the stage for bound state analysis.

Contribution

It introduces a functional RG approach to 2D QCD, deriving comprehensive flow equations for gauge and fermion interactions, and explores symmetry and group variations.

Findings

Flow equations exhibit expected super-renormalizable behavior in UV.

Infrared regime shows strong coupling effects.

Framework facilitates future bound state spectrum studies.

Abstract

Quantum Chromodynamics in two spacetime dimensions is investigated with the Functional Renormalization Group. We use a functional formulation with covariant gauge fixing and derive Renormalization Group flow equations for the gauge coupling, quark mass and an algebraically complete set of local fermion-fermion interaction vertices. The flow, based on a convenient Callan-Symanzik-type regularization, shows the expected behavior for a super-renormalizable theory in the ultraviolet regime and leads to a strongly coupled regime in the infrared. Through a detailed discussion of symmetry implications, and variations in the gauge group and flavor numbers, the analysis sets the stage for a more detailed investigation of the bound state spectrum in future work.