New gaugings and non-geometry

Abstract

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. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non-toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the $SO(4)$ gaugings to an infinite discrete set and excludes all the $SO(8)$ gaugings other than the standard one.

arXiv comment47 pages

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• Consistent 4-form fluxes for maximal supergravity
• From Binary Error Correcting Codes to a Relation Between Maximal D=4 and D=3 Supergravities