On Partially Massless Theory in 3 Dimensions

TL;DR

This paper investigates the conditions under which a three-dimensional bigravity model exhibits partial masslessness, concluding that it generally does not, except in special backgrounds where additional symmetries temporarily appear.

Contribution

It provides a detailed canonical analysis showing that partial masslessness in drei-dreibein gravity depends on the stability condition of secondary constraints, clarifying when such symmetries can emerge.

Findings

Partial masslessness generally does not occur in the model.

Special backgrounds can temporarily exhibit additional symmetries.

Additional symmetries disappear at quadratic order in perturbations.

Abstract

We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. We provide a thorough canonical analysis and identify that whether the theory becomes partially massless depends on the form of the stability condition of the secondary constraint responsible for the absence of the ghost. Generically, it is found to be an equation for a Lagrange multiplier implying that partially massless zwei-dreibein gravity does not exist. However, for special backgrounds this condition is identically satisfied leading to the presence of additional symmetries, which however disappear at quadratic order in perturbations.