Electric-magnetic deformations of D=4 gauged supergravities

TL;DR

This paper explores the structure of duality and symplectic deformations in four-dimensional gauged supergravity theories, revealing when such deformations are trivial or non-trivial across various models and gaugings.

Contribution

It introduces a general framework for computing symplectic deformations, classifies duality orbits, and clarifies the triviality or non-triviality of deformations like the omega parameter in different supergravity models.

Findings

No continuous deformations for Fayet-Iliopoulos gaugings of N=2 STU model.

Omega deformation is classically trivial in certain N=2 models.

Omega parameter can be dualized away in N=6 truncation but not in N=2 twin truncation.

Abstract

We discuss duality orbits and symplectic deformations of D=4 gauged supergravity theories, with focus on N$\ge$2. We provide a general constructive framework for computing symplectic deformations starting from a reference gauging, and apply it to many interesting examples. We prove that no continuous deformations are allowed for Fayet-Iliopoulos gaugings of the N=2 STU model and in particular that any $\omega$ deformation is classically trivial. We further show that although in the N=6 truncation of SO(8) maximal supergravity the $\omega$ parameter can be dualized away, in the 'twin' N=2 truncation $\omega$ is preserved and a second, new deformation appears. We further provide a full classification and appropriate duality orbits of certain N=4 gauged supergravities, including all inequivalent SO(4)$^2$ gaugings and several non-compact forms.