Higher spin super-Cotton tensors and generalisations of the linear-chiral duality in three dimensions

TL;DR

This paper develops duality transformations for higher spin super-Cotton tensors in three dimensions, extending known dualities to supersymmetric and higher spin theories, and relates these to conformal geometry and existing dualities.

Contribution

It introduces new duality transformations for higher spin superconformal theories in three dimensions, generalizing linear-chiral duality and extending it to supersymmetric and non-supersymmetric cases.

Findings

Duality relates higher-derivative theories to two-derivative models.

Constructs gauge prepotentials and super-Cotton tensors for various superspins.

Connects higher spin conformal geometry to known Cotton tensors via N=1 to N=0 reduction.

Abstract

In three spacetime dimensions, (super)conformal geometry is controlled by the (super) Cotton tensor. We present a new duality transformation for N-extended supersymmetric theories formulated in terms of the linearised super-Cotton tensor or its higher spin extensions for the cases N=2, 1, 0. In the N=2 case, this transformation is a generalisation of the linear-chiral duality, which is known to provide a dual description in terms of chiral superfields for general models of self-interacting N=2 vector multiplets in three dimensions and N=1 tensor multiplets in four dimensions. For superspin-1 (gravitino multiplet), superspin-3/2 (supergravity multiplet) and higher superspins s>3/2, the duality transformation relates a higher-derivative theory to one containing at most two derivatives at the component level. In the N=1 case, we introduce gauge prepotentials for higher spin superconformal gravity and construct the corresponding super-Cotton tensors, as well as the higher spin extensions of the linearised N=1 conformal supergravity action. Our N=1 duality transformation is a higher spin extension of the known superfield duality relating the massless N=1 vector and scalar multiplets. In the non-supersymmetric (N=0) case, the gauge prepotentials for higher spin conformal geometry (both bosonic and fermionic) and the corresponding Cotton tensors can be obtained from their N=1 counterparts by carrying out N=1 --> N=0 reduction. In the bosonic sector, this reduction is shown to lead to the Cotton tensors for higher spins constructed by Pope and Townsend, and by Damour and Deser in the spin-3 case. Our N=0 duality transformation is a higher spin extension of the vector-scalar duality.