Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory

TL;DR

This paper introduces a novel method using abelian color cycles to reformulate non-abelian lattice gauge theories, enabling new strong coupling expansions and dual representations that facilitate potential simulations.

Contribution

The paper develops the abelian color cycle approach for non-abelian gauge theories, providing a systematic way to derive strong coupling series and dual representations, including for SU(2) with fermions.

Findings

Derived a closed-form strong coupling series for SU(2) gauge theories.

Identified constraints for dual variables in the SU(2) case.

Discussed potential for dual simulations and generalization to other groups.

Abstract

We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over "abelian color cycles" (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).