Dyonic ISO(7) supergravity and the duality hierarchy

TL;DR

This work provides a comprehensive, four-dimensional perspective on maximal ${\cal N}=8$ supergravity with a dyonic ISO(7) gauging, showing how a consistent ISO(7)$_c$ truncation emerges from the embedding-tensor formalism and duality hierarchy while embedding into massive type IIA on S^6. It constructs an explicit bosonic Lagrangian, a restricted yet closed duality hierarchy, and several highly informative truncations to ${\cal N}=2$ and ${\cal N}=1$ sectors with SU(3), G$_2$, and SO(4) symmetry, including canonical and superpotential formulations. The analysis uncovers a rich AdS vacuum structure, including a new ${\cal N}=1$ SU(3) point and multiple non-supersymmetric but perturbatively stable vacua, all of which persist in the full ${\cal N}=8$ theory and many of which have higher-dimensional interpretations. Overall, the paper advances the understanding of deformations in maximal gauged supergravity, clarifies the role of dyonic gaugings in the vacuum landscape, and provides concrete truncations with potential holographic significance.

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.