Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model

TL;DR

This paper establishes a duality between 3D SU(2) lattice gauge theory and the Ponzano-Regge model of 3D gravity, revealing new insights into their mathematical relationship and potential applications to other non-abelian models.

Contribution

It derives a duality transform linking 3D SU(2) lattice gauge theory with the Ponzano-Regge model, including explicit character expansion and integration techniques.

Findings

Partition function expressed in terms of 6j symbols

Dual of Ponzano-Regge model is an SU(2) lattice gauge theory with constrained plaquettes

Techniques applicable to other non-abelian models in any dimension

Abstract

By carrying out character expansion and integration over all link variables, the partition function of 3-dimensional pure SU(2) lattice gauge theory is rewritten in terms of 6j symbols. The result is Ponzano-Regge model of 3-dimensional gravity with a term that explicitly breaks general coordinate invariance. Conversely, we show that dual of Ponzano-Regge model is an SU(2) lattice gauge theory where all plaquette variables are constrained to the identity matrix and therefore the model needs no further regularization. Our techniques are applicable to other models with non-abelian symmetries in any dimension and provide duality transform for the partition function.