# From topological to topologically massive gravity through the gauge principle

## TL;DR

This paper demonstrates how applying the gauge principle to a non-dynamical fermion matter sector induces a topologically massive gravity with local propagating degrees of freedom in three dimensions.

## Contribution

It introduces a novel method to generate topologically massive gravity by gauging a global symmetry in a non-dynamical fermion model, leading to a gravitational Chern-Simons term.

## Key findings

- Gauging the global symmetry adds a vector-spinor field.
- Integrating out the spin-3/2 field yields a gravitational Chern-Simons term.
- The resulting theory exhibits local propagating degrees of freedom.

## Abstract

It is well known that three-dimensional Einstein's gravity without matter is topological, i.e. it does not have local propagating degrees of freedom. The main result of this work is to show that dynamics in the gravitational sector can be induced by employing the gauge principle on the matter sector. This is described by a non-dynamical fermion model that supports a global gauge symmetry. By gauging this symmetry, a vector-spinor field is added to the original action to preserve the local gauge invariance. By integrating out this spin-3/2 field, we obtain a gravitational Chern-Simons term that gives rise to local propagating degrees of freedom in the gravitational sector. This is defined, after the gauging, by topologically massive gravity.