Imaginary supergravity or Virial supergravity?

TL;DR

This paper introduces a novel supergravity theory based on gauging the Virial supercurrent supermultiplet, featuring unique properties like unimodular metrics and non-geometrical connections, expanding the classification of $ =1$ supergravities.

Contribution

It constructs a new type of supergravity from the Virial supercurrent supermultiplet, providing a full superspace action and exploring its unique features and matter couplings.

Findings

Supergravity with unimodular metric and non-geometrical connection.

Full non-linear superspace action constructed.

Examples of matter couplings and higher derivative terms studied.

Abstract

When a globally supersymmetric theory is scale invariant, it must possess a Virial supercurrent supermultiplet. The multiplet structure is analogous to the R-current supermultiplet in globally R-symmetric theories but we put extra "$i$"s in various formulae. We construct a novel type of supergravity from gauging the Virial supercurrent supermultiplet in $d=1+3$ dimensions. We give the full non-linear superspace action with the help of a covariantly linear unitary superconformal compensator. The resulting supergravity is peculiar: (1) no Einstein-like second order kinetic term is allowed without matter (2) there exists a dynamical non-geometrical connection (3) the metric is unimodular in the Wess-Zumino gauge and can be coupled only to scale invariant matter. Examples of matter couplings and higher derivative kinetic terms are studied from the superconformal approach. Our work completes the classification of the irreducible $\mathcal{N}=1$ supergravities in $d=1+3$ dimensions.