A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical Fermions

TL;DR

This paper introduces a local, exact dual algorithm for lattice Yang-Mills theory coupled with dynamical fermions, extending previous pure gauge methods to include fermionic matter using a polymer expansion approach.

Contribution

The authors develop a new ergodic Metropolis algorithm for lattice gauge theories with fermions, applicable to various groups and dimensions, incorporating a polymer expansion for the fermion determinant.

Findings

Algorithm is local, exact, and gauge-invariant.

Applicable to SU(2) in three dimensions with staggered fermions.

Addresses the challenge of negative amplitudes in the polymer expansion.

Abstract

We extend the dual algorithm recently described for pure, non-abelian Yang-Mills on the lattice to the case of lattice fermions coupled to Yang-Mills, by constructing an ergodic Metropolis algorithm for dynamic fermions that is local, exact, and built from gauge-invariant boson-fermion coupled configurations. For concreteness, we present in detail the case of three dimensions, for the group SU(2) and staggered fermions, however the algorithm readily generalizes with regard to group and dimension. The treatment of the fermion determinant makes use of a polymer expansion; as with previous proposals making use of the polymer expansion in higher than two dimensions, the critical question for practical applications is whether the presence of negative amplitudes can be managed in the continuum limit.