# Approximate dual representation for Yang-Mills SU(2) gauge theory

## TL;DR

This paper introduces an approximate dual representation for SU(2) lattice gauge theory using plaquette occupation numbers, enabling efficient Monte Carlo simulations that match traditional methods in accuracy.

## Contribution

It develops a novel dual variable formulation for non-Abelian gauge theories and demonstrates its effectiveness through Monte Carlo simulations and comparison with standard algorithms.

## Key findings

- Good agreement with traditional algorithms in strong and weak coupling regimes
- Deviations below 0.1% for certain coupling ranges
- Accurate calculation of the lightest glueball mass

## Abstract

An approximate dual representation for non-Abelian lattice gauge theories in terms of a new set of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang-Mills action. After studying the constraints due to gauge symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a PONs configuration the weight factor is given by Haar-measure integrals over all links whose integrands are products of powers of plaquettes. Herein, updates are limited to changes of the PON at a plaquette or all PONs on a coordinate plane. The Markov chain transition probabilities are computed employing truncated maximal trees and the Metropolis algorithm. The algorithm performance is investigated with different types of updates for the plaquette mean value over a large range of $\beta$s. Using a $12^4$ lattice very good agreement with a conventional heath bath algorithm is found for the strong and weak coupling limits. Deviations from the latter being below 0.1% for $2.5 < \beta < 3$. The mass of the lightest $J^{PC}=0^{++}$ glueball is evaluated and reproduces the results found in the literature.