Induced QCD I: Theory

TL;DR

This paper investigates an alternative lattice discretization of SU(N_c) Yang-Mills theory using auxiliary boson fields, extending theoretical proofs and deriving bounds to support its equivalence to standard continuum Yang-Mills theory.

Contribution

It extends the proof of continuum limit equivalence to SU(N_c), refines bounds on auxiliary fields, and performs perturbative matching of parameters in the induced gauge theory.

Findings

Proved continuum limit reproduces Yang-Mills in 2D for SU(N_c)

Derived bounds on auxiliary boson fields for non-integer N_b

Performed perturbative calculation to match lattice coupling

Abstract

We explore an alternative discretization of continuum SU(N_c) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N_b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N_b can be as small as N_c. In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N_c) to SU(N_c), (ii) derive refined bounds on N_b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.