# Induced QCD II: Numerical results

## TL;DR

This paper numerically tests an alternative lattice discretization of SU(N) Yang-Mills theory, showing it reproduces known continuum results in three dimensions and confirming the theoretical bounds for auxiliary fields.

## Contribution

It provides numerical evidence supporting the induced gauge theory discretization's validity in three dimensions and refines the bounds on auxiliary fields needed for continuum equivalence.

## Key findings

- Observables match between induced and standard actions within lattice artifacts.
- Bound for auxiliary fields can be relaxed from N_c - 3/4 to N_c - 5/4.
- Supports the conjecture that the induced theory reproduces continuum SU(N) Yang-Mills in higher dimensions.

## Abstract

We numerically explore an alternative discretization of continuum $\text{SU}(N_c)$ Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group $\text{U}(N_c)$. This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over $N_b$ auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum $\text{SU}(N_c)$ Yang-Mills theory in $d=2$ dimensions if $N_b$ is larger than $N_c-\frac{3}{4}$ and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for $d>2$. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group $\text{SU}(2)$ in three dimensions. We show that observables computed in the induced theory, such as the static $q\bar q$ potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find that the bound for $N_b$ can be relaxed to $N_c-\frac{5}{4}$ as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.