Conformal supergravity in three dimensions: New off-shell formulation

TL;DR

This paper introduces a new off-shell formulation for N-extended conformal supergravity in three dimensions, utilizing superspace gauging of the superconformal algebra, with the super Cotton tensor as a key curvature superfield.

Contribution

It presents a novel off-shell superspace formulation for three-dimensional conformal supergravity, linking the super Cotton tensor to the algebra of covariant derivatives.

Findings

Curved superspace is conformally flat iff the super Cotton tensor vanishes.

The formulation reduces to the conventional one with SL(2,R) x SO(N) structure group.

The approach simplifies the understanding of supergravity constraints.

Abstract

We propose a new off-shell formulation for N-extended conformal supergravity in three spacetime dimensions. Our construction is based on the gauging of the N-extended superconformal algebra in superspace. Covariant constraints are imposed such that the algebra of covariant derivatives is given in terms of a single curvature superfield which turns out to be the super Cotton tensor. An immediate corollary of this construction is that the curved superspace is conformally flat if and only if the super Cotton tensor vanishes. Upon degauging of certain local symmetries, our formulation is shown to reduce to the conventional one with the local structure group SL(2,R) x SO(N).