Dyonic ISO(7) supergravity and the duality hierarchy

Understand

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.