GR uniqueness and deformations

TL;DR

This paper explores how changing the Lorentz group representation for gravitons from parity symmetric to chiral leads to a family of gravity theories with second order equations, sharing some amplitudes with General Relativity but differing in others.

Contribution

It demonstrates that using a chiral representation instead of the symmetric one results in an infinite-parametric family of gravity theories, breaking the uniqueness of General Relativity.

Findings

GR is unique with parity symmetric representation.

Chiral representation leads to multiple consistent gravity theories.

All theories share GR's MHV amplitudes but differ in all same helicity amplitudes.

Abstract

In the metric formulation gravitons are described with the parity symmetric $S_+^2\otimes S_-^2$ representation of Lorentz group. General Relativity is then the unique theory of interacting gravitons with second order field equations. We show that if a chiral $S_+^3\otimes S_-$ representation is used instead, the uniqueness is lost, and there is an infinite-parametric family of theories of interacting gravitons with second order field equations. We use the language of graviton scattering amplitudes, and show how the uniqueness of GR is avoided using simple dimensional analysis. The resulting distinct from GR gravity theories are all parity asymmetric, but share the GR MHV amplitudes. They have new all same helicity graviton scattering amplitudes at every graviton order. The amplitudes with at least one graviton of opposite helicity continue to be determinable by the BCFW recursion.