Dualization of non-abelian lattice gauge theory with Abelian Color Cycles (ACC)

TL;DR

This paper introduces a novel dualization method for non-abelian lattice gauge theories using Abelian Color Cycles, enabling exact strong coupling expansions for SU(2) and SU(3) models.

Contribution

It presents a new ACC-based approach that simplifies non-abelian gauge theories into a form similar to abelian cases, allowing exact dual representations.

Findings

Exact strong coupling series for SU(2) and SU(3) lattice gauge theories.

Closed-form gauge integrals in the dual representation.

Potential for improved computational techniques in non-abelian gauge theories.

Abstract

We discuss a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theories. The Wilson gauge action is decomposed into a sum over "abelian color cycles" (ACC), which are loops around plaquettes visiting different colors at the corners. ACCs are complex numbers and thus commute such that a dual representation of a non-abelian theory can be obtained as in the abelian case. We apply the ACC approach to SU(2) and SU(3) lattice gauge theory and exactly rewrite the two partition sums in a strong coupling series where all gauge integrals are known in closed form.