Trivial symmetries in a 3D topological torsion model of gravity

TL;DR

This paper investigates gauge symmetries in a 2+1 dimensional gravity model, demonstrating that different symmetry sets are equivalent up to trivial symmetries, clarifying their relationship.

Contribution

It shows that two seemingly different sets of gauge symmetries in a topological gravity model are actually equivalent, differing only by trivial symmetries.

Findings

Different gauge symmetry sets are canonically equivalent.

Trivial symmetries account for the apparent differences.

Clarifies the structure of gauge symmetries in 3D gravity.

Abstract

We study the gauge symmetries in a Mielke-Baekler type model of gravity in 2+1 dimensions. The model is built in a Poincare gauge theory framework where localisation of Poincare symmetries lead to gravity. However, explicit construction of gauge symmetries in the model through a Hamiltonian procedure yields an apparently different set of symmetries, as has been noted by various authors. Here, we show that the two sets of symmetries are actually equivalent in a canonical sense, their difference being just a set of trivial symmetries.