Duals of nonabelian gauge theories in $D$ dimensions

TL;DR

This paper derives a local dual representation for nonabelian lattice gauge theories in D dimensions, enabling new analytical and simulation approaches, especially in strong and weak coupling regimes.

Contribution

It introduces a local dual formulation of nonabelian gauge theories in arbitrary dimensions, with explicit actions for D ≤ 4, enhancing analytical and computational methods.

Findings

Dual theory is local in the eigenspace of Casimir operators.

Explicit action form provided for D ≤ 4.

Potential for improved strong and weak coupling simulations.

Abstract

The dual of an arbitrary $D$-dimensional nonabelian lattice gauge theory, obtained after character expansion and integration over the gauge group, is shown to be a {\em local} lattice theory in the eigenspace of the Casimir operators. For $D\leq4$ we also provide the explicit form of the action as a product of character expansion coefficients and Racah coefficients. The representation can be used to facilitate strong coupling expansions. Furthermore, the possibility of simulations, at weak coupling, in the dual representation, is also discussed.