Gauge Symmetries, Exact Symmetries and Conserved Charges in Minimal Massive Gravity

TL;DR

This paper explores the gauge symmetries and conserved charges in Minimal Massive Gravity, revealing a new transformation mechanism for auxiliary fields and establishing a gauge-invariant charge in specific parameter regimes.

Contribution

It introduces a novel transformation compatible with Wald's approach for auxiliary fields, extending the understanding of symmetries and conserved charges in MMG.

Findings

Identification of three gauge symmetries with closed algebras

Development of a new transformation for auxiliary fields

Derivation of a gauge-invariant conserved charge

Abstract

In this paper, we investigate a three-dimensional gravitational model known as Minimal Massive Gravity (MMG), which includes an auxiliary field, using the covariant phase space method. Our analysis reveals the presence of three gauge symmetries whose algebras close via field recombination and parameter classification within this framework. Upon incorporating these additional symmetries within a specific limit of parameters, we find that the Kosmann derivative should be replaced by a novel transformation compatible with Wald's approach, which establishes a new mechanism for generating exact symmetries and constructing their corresponding conserved charge in theories with auxiliary fields, extending beyond standard methods. However, this transformation does not yield closed algebras on the space of fundamental fields. We find that this corresponds to a Lorentz vector that characterizes the approximate completeness of translation symmetry. As a result, we obtain a gauge invariant charge at a certain limit of parameters, which emerges as a nontrivial combination of the diffeomorphism charge and integrable gauge charges.