Current Status of the Numerical Simulations of d=3 SU(2) Lattice Gauge Theory in the Dual Formulation

TL;DR

This paper reports on ongoing numerical simulations of 3D SU(2) lattice gauge theory in the dual formulation, addressing implementation, sign problem, ergodicity, observable measurement, and thermalization challenges.

Contribution

It introduces improved techniques for dual formulation simulations and provides a comprehensive analysis of current challenges and potential solutions.

Findings

Enhanced quasi-local updating methods

Detailed analysis of the sign problem

Insights into ergodicity and thermalization issues

Abstract

We have continued our systematic investigations of the numerical simulations of lattice gauge theories in the dual formulation. These include: i) a more practical implementation of the quasi-local updating technique, ii) a thorough investigation of the sign problem, iii) issues related to the ergodicity of the various update algorithms, iv) a novel way of measuring conventional observables like plaquette in the dual formalism and v) investigations of thermalisation. While the dual formulation holds out a lot of promises in principle, there are still some ways to go before it can be made into an attractive alternative lattice formulation.