An Exotic Theory of Massless Spin-Two Fields in Three Dimensions

TL;DR

This paper introduces a novel deformation of the Pauli-Fierz action in three dimensions, allowing for PT non-invariant terms and resulting in a different gauge algebra, enabling consistent interactions among multiple massless spin-two fields.

Contribution

It demonstrates a new class of deformations in three-dimensional massless spin-two theories that go beyond general relativity by relaxing PT invariance.

Findings

A new gauge algebra different from diffeomorphisms

Existence of PT non-invariant deformations in 3D

Consistent interactions among multiple massless spin-two fields

Abstract

It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one allows for PT non-invariant terms. The new gauge algebra is different from that of diffeomorphisms. Furthermore, this deformation can be generalized to the case of a collection of massless spin-two fields. In this case it describes a consistent interaction among them.