Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms

TL;DR

This paper systematically analyzes the symmetries of 3D topological gravity with torsion in both Hamiltonian and Lagrangian formalisms, clarifying the relationship between spacetime and gauge symmetries.

Contribution

It provides a detailed comparison of symmetry structures in different formalisms, highlighting the inequivalence of Poincare gauge and gauge symmetries in the first order formalism.

Findings

Poincare gauge symmetries are inequivalent to gauge symmetries in the action.

Diffeomorphism symmetry is equivalent to gauge symmetry in the metric formulation.

The analysis connects spacetime symmetries with gauge transformations in topological gravity.

Abstract

A systematic analysis of the symmetries of topological 3D gravity with torsion and a cosmological term, in the first order formalism, has been performed in details - both in the hamiltonian and lagrangian formalisms. This illuminates the connection between the symmetries of curved spacetime (diffeomorphisms plus local Lorentz transformations) with the Poincare gauge transformations. The Poincare gauge symmetries of the action are shown to be inequivalent to its gauge symmetries. Finally, the complete analysis is compared with the metric formulation where the diffeomorphism symmetry is shown to be equivalent to the gauge symmetry.