Dyonic ISO(7) supergravity and the duality hierarchy

TL;DR

This paper analyzes the structure and vacua of dyonic ISO(7) gauged supergravity in four dimensions, revealing a rich landscape of stable AdS vacua, including new solutions, through detailed Lagrangian and hierarchy studies.

Contribution

It provides a comprehensive formulation of the dyonic ISO(7) supergravity, including tensor hierarchies, truncations, and vacuum analysis, highlighting new stable AdS vacua not seen in purely electric gaugings.

Findings

Discovery of a new  vacuum with SU(3) symmetry

Identification of multiple stable non-supersymmetric vacua

Complete characterization of the vacuum structure and spectra

Abstract

Motivated by its well defined higher dimensional origin, a detailed study of $D=4$ $\mathcal{N}=8$ supergravity with a dyonically gauged $\textrm{ISO}(7) = \textrm{SO}(7) \ltimes \mathbb{R}^7$ gauge group is performed. We write down the Lagrangian and describe the tensor and duality hierarchies, focusing on an interesting subsector with closed field equations and supersymmetry transformations. We then truncate the $\mathcal{N}=8$ theory to some smaller sectors with $\mathcal{N}=2$ and $\mathcal{N}=1$ supersymmetry and SU(3), $\textrm{G}_2$ and SO(4) bosonic symmetry. Canonical and superpotential formulations for these sectors are given, and their vacuum structure and spectra is analysed. Unlike the purely electric ISO(7) gauging, the dyonic gauging displays a rich structure of vacua, all of them AdS. We recover all previously known ones and find a new $\mathcal{N}=1$ vacuum with SU(3) symmetry and various non-supersymmetric vacua, all of them stable within the full $\mathcal{N}=8$ theory.