The dual of pure non-Abelian lattice gauge theory as a spin foam model

TL;DR

This paper develops an exact duality transformation for pure non-Abelian lattice gauge theories, transforming them into spin foam models that are more tractable in different coupling regimes.

Contribution

It provides a general duality mapping for non-Abelian gauge theories on lattices of any dimension, explicitly performing all group integrations and relating gauge theories to spin foam models.

Findings

Duality maps strong coupling to weak coupling regimes.

Partition functions and Wilson loop expectations are expressed via finite-dimensional representations.

Dual models are spin foam systems in statistical mechanics.

Abstract

We derive an exact duality transformation for pure non-Abelian gauge theory regularized on a lattice. The duality transformation can be applied to gauge theory with an arbitrary compact Lie group G as the gauge group and on Euclidean space-time lattices of dimension d >= 2. It maps the partition function as well as the expectation values of generalized non-Abelian Wilson loops (spin networks) to expressions involving only finite-dimensional unitary representations, intertwiners and characters of G. In particular, all group integrations are explicitly performed. The transformation maps the strong coupling regime of non-Abelian gauge theory to the weak coupling regime of the dual model. This dual model is a system in statistical mechanics whose configurations are spin foams on the lattice.