On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories

TL;DR

This paper explores higher-derivative equations in 3D gravity and higher spin theories, revealing new equivalences, a non-unitary gravity model with a fifth-order term, and a novel unitary spin-3 gauge theory.

Contribution

It introduces new higher-derivative gauge-invariant equations for arbitrary spins, including a non-unitary gravity model and a unitary spin-3 theory, expanding the understanding of 3D higher spin gauge theories.

Findings

Recovered known equivalences for spins 1 and 2

Discovered a non-unitary 5th order gravity theory in 3D

Proposed a new unitary 6th order gauge theory for spin 3

Abstract

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3.