Renormalization of two-dimensional XQCD

TL;DR

This paper investigates the renormalization of two-dimensional Extended QCD (XQCD) in the large N_c limit, demonstrating how auxiliary scalar fields become dynamical and dominate low-energy physics without altering physical observables.

Contribution

It provides a detailed analysis of the renormalization group flow of 2D XQCD, showing the emergence of dynamical scalar fields and their impact on low-energy behavior.

Findings

Scalar fields become dynamical with kinetic terms.

Parity-odd parts dominate at low energy.

Physical observables remain unchanged.

Abstract

Recently, Kaplan proposed an interesting extension of QCD named Extended QCD or XQCD with bosonic auxiliary fields [1]. While its partition function is kept exactly the same as that of QCD, XQCD naturally contains properties of low-energy hadrons. We apply this extension to the two-dimensional QCD in the large $N_c$ limit ('t Hooft model) [2]. In this solvable model, it is possible to directly examine the hadronic picture of the 2d XQCD and analyze its renormalization group flow to understand how the auxiliary degrees of freedom behave in the low energy region. We confirm that the additional scalar fields can become dynamical acquiring the kinetic term, and its parity-odd part becomes dominant in the low energy region. This renomalization of XQCD provides an "extension" of the renormalization scheme of QCD, inserting different field variables from those in the original theory, without any changes in physical observables.