New gaugings and non-geometry

Understand

We discuss the possible realisation in string/M theory of the recently discovered family of four-dimensional maximal $SO(8)$ gauged supergravities, and of an analogous family of seven-dimensional half-maximal $SO(4)$ gauged supergravities.

• We first prove a no-go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten- or eleven-dimensional supergravity.
• In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated.
• Introducing the minimal number of additional coordinates possible, we then show that the standard $S^3$ and $S^7$ compactifications of ten- and eleven-dimensional supergravity admit a new class of section-violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the $SO(4)$ and $SO(8)$ gaugings respectively.