Minimal $\cal N=4$ topologically massive supergravity

TL;DR

This paper constructs a minimal off-shell $ =4$ supergravity model using a single vector multiplet, challenging the belief that two are necessary, and explores its solutions and dual formulations.

Contribution

It introduces a novel off-shell $ =4$ supergravity model with a single compensating multiplet, providing new insights into supergravity constructions with eight supercharges.

Findings

Constructed a minimal off-shell $ =4$ supergravity model.

Identified solutions including critical (4,0) anti-de Sitter superspaces.

Proposed a dual formulation with hypermultiplet replacement.

Abstract

Using the superconformal framework, we construct a new off-shell model for $\cal N=4$ topologically massive supergravity which is minimal in the sense that it makes use of a single compensating vector multiplet and involves no free parameter. As such, it provides a counterexample to the common lore that two compensating multiplets are required within the conformal approach to supergravity with eight supercharges in diverse dimensions. This theory is an off-shell $\cal N=4$ supersymmetric extension of chiral gravity. All of its solutions correspond to non-conformally flat superspaces. Its maximally supersymmetric solutions include the so-called critical (4,0) anti-de Sitter superspace introduced in arXiv:1205.4622, and well as warped critical (4,0) anti-de Sitter superspaces. We also propose a dual formulation for the theory in which the vector multiplet is replaced with an off-shell hypermultiplet. Upon elimination of the auxiliary fields belonging to the hypermultiplet and imposing certain gauge conditions, the dual action reduces to the one introduced in arXiv:1605.00103.