Duality of parity doublets of helicity $\pm 2$ in $D=2+1$

TL;DR

This paper explores the duality relationships among various models describing helicity ±2 parity singlets in 2+1 dimensions, revealing how soldering and master actions connect these models to the linearized BHT massive gravity.

Contribution

It demonstrates the duality between higher-order models and the linearized BHT theory using soldering and master actions in 2+1 dimensions.

Findings

Soldering of fourth-order models yields the linearized BHT gravity.

A triple master action connects dual models and the BHT theory.

Dual maps between models are established through gauge-invariant correlators.

Abstract

In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\pm 1$, namely the self-dual model of first-order (in derivatives) and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for helicity $\pm 2$ there are four models $S_{SD\pm}^{(r)}$ describing parity singlets of helicities $\pm 2$. They are of first-, second-,third- and fourth-order ($r=1,2,3,4$) respectively. Here we show that the generalized soldering of the opposite helicity models $S_{SD+}^{(4)}$ and $S_{SD-}^{(4)}$ leads to the linearized form of the new massive gravity suggested by Bergshoeff, Hohm and Townsend (BHT) similarly to the soldering of $S_{SD+}^{(3)}$ and $S_{SD-}^{(3)}$. We argue why in both cases we have the same result. We also find out a triple master action which interpolates between the three dual models: linearized BHT theory, $S_{SD+}^{(3)} + S_{SD-}^{(3)}$ and $S_{SD+}^{(4)} + S_{SD-}^{(4)}$. By comparing gauge invariant correlation functions we deduce dual maps between those models. In particular, we learn how to decompose the field of the linearized BHT theory in helicity eigenstates of the dual models up to gauge transformations.