# Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint

## TL;DR

This paper uses the Faddeev-Jackiw symplectic method to analyze the gauge symmetries, constraints, and degrees of freedom in topologically massive AdS gravity, providing an alternative approach to its dynamical study.

## Contribution

It systematically identifies gauge symmetries and constraints in topologically massive AdS gravity using the symplectic approach and computes the physical degrees of freedom.

## Key findings

- Identifies gauge symmetries via zero-modes of the symplectic matrix.
- Calculates the generalized Faddeev-Jackiw brackets for the model.
- Confirms the model has one physical degree of freedom.

## Abstract

By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant $\Lambda$, elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via an appropriate partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.