The dual of non-Abelian Lattice Gauge Theory

TL;DR

This paper establishes an exact duality between non-Abelian lattice gauge theories and spin foam models, transforming group variables into combinatorial data involving irreducible representations and intertwiners, applicable to various observables.

Contribution

It introduces a novel strong-weak duality transformation for non-Abelian lattice gauge theories, linking them to spin foam models with explicit combinatorial expressions.

Findings

Duality transformation applies to partition functions and observables

Group degrees of freedom are replaced by irreducible representations

The dual formulation simplifies the analysis of gauge theories

Abstract

Non-Abelian Lattice Gauge Theory in Euclidean space-time of dimension d>=2 whose gauge group is any compact Lie group is related to a Spin Foam Model by an exact strong-weak duality transformation. The group degrees of freedom are integrated out and replaced by combinatorial expressions involving irreducible representations and intertwiners of the gauge group. This transformation is available for the partition function, for the expectation value of observables (spin networks), and for the correlator of centre monopoles which is a ratio of partition functions in the original model and an ordinary expectation value in the dual formulation.