Lattice Chern-Simons Gravity via Ponzano-Regge Model

TL;DR

This paper introduces a lattice formulation of Chern-Simons gravity that aligns with the Ponzano-Regge model, providing a discrete approach that preserves key symmetries and converges to the continuum theory.

Contribution

It presents a novel lattice action for Chern-Simons gravity that is invariant under local Lorentz and gauge diffeomorphisms, connecting to the Ponzano-Regge model.

Findings

Partition function matches Ponzano-Regge model

Lattice action reproduces continuum Chern-Simons gravity

Invariance under lattice local Lorentz and gauge diffeomorphism

Abstract

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.