Recent Developments in Dual Lattice Algorithms

TL;DR

This paper reviews recent advances in dual lattice algorithms for SU(2) gauge theories, highlighting algorithm validation, incorporation of dynamical fermions, and addressing challenges like critical slowing down and the sign problem.

Contribution

It provides a comprehensive review of dual lattice algorithms for SU(2) gauge theories, including new methods for dynamical fermions and analysis of current challenges.

Findings

Validation of dual algorithms against conventional simulations in D=3.

Incorporation of local, exact dynamical fermion algorithms into the dual framework.

Discussion of challenges such as critical slowing down and the sign problem.

Abstract

We review recent progress in numerical simulations with dually transformed SU(2) LGT, starting with a discussion of explicit dual amplitudes and algorithms for SU(2) pure Yang Mills in D=3 and D=4. In the D=3 case, we discuss results that validate the dual algorithm against conventional simulations. We also review how a local, exact dynamical fermion algorithm can naturally be incorporated into the dual framework. We conclude with an outlook for this technique and a look at some of the current challenges we've encountered with this method, specifically critical slowing down and the sign problem.