Induced YM theory with auxiliary bosons

TL;DR

This paper investigates an alternative lattice gauge theory formulation using auxiliary bosons, deriving conditions for continuum limit equivalence to Yang-Mills theory and comparing coupling relations with numerical results.

Contribution

It introduces an induced gauge action with auxiliary bosons, derives continuum limit conditions, and computes the coupling relation, showing agreement with numerical data.

Findings

Continuum limit conditions for the induced gauge theory are established.

Perturbative coupling relations match numerical results for N=2 in 3D.

The auxiliary boson formulation offers a viable alternative to Wilson's approach.

Abstract

We study pure SU(N) lattice gauge theory with a plaquette weight factor given by an inverse determinant which can be written as an integral over auxiliary bosonic fields (modifying a proposal of Budczies and Zirnbauer). We derive conditions for the existence of a continuum limit and its equivalence to Yang-Mills theory. Furthermore, we perturbatively compute the relation between the coupling constants of the `induced' gauge action and the familiar Wilson gauge action using the background-field technique. The perturbative relation agrees well with numerical results for N=2 in three dimensions.