Exceptional Flux Compactifications

Abstract

We consider type II (non-)geometric flux backgrounds in the absence of brane sources, and construct their explicit embedding into maximal gauged D=4 supergravity. This enables one to investigate the critical points, mass spectra and gauge groups of such backgrounds. We focus on a class of type IIA geometric vacua and find a novel, non-supersymmetric and stable AdS vacuum in maximal supergravity with a non-semisimple gauge group. Our construction relies on a non-trivial mapping between SL(2) x SO(6,6) fluxes, SU(8) mass spectra and gaugings of E7(7) subgroups.

Figures (2)

• Figure 1: Starting from gauged maximal supergravity (box --1-- in the above diagram), one can move step by step downwards or towards the right by performing group-theoretical truncations which are described below in detail. The labels $S$, $T$ and $U$ are introduced in order to keep track of the different group factors along the truncations.
• Figure 2: Diagram of the two-step lifting of $\,{\cal N}=1\,$ flux backgrounds firstly to $\,{\cal N}=4\,$ by removing the $\,\textrm{SO}(3)\,$ truncation and secondly to $\,{\cal N}=8\,$ by removing the $\,\mathbb{Z}_2\,$ orientifold projection. As depicted in the figure, only a subset of $\,{\cal N}=4\,$ theories can be truncated to $\,{\cal N}=1\,$ theories via an $\,\textrm{SO}(3)\,$ truncation. On the other hand, only a subset of $\,{{\cal N}=4}$ theories can be obtained from $\,{\cal N}=8\,$ supergravity via a $\,\mathbb{Z}_{2}\,$ orientifold projection. The relevant fact is that the intersection between these two subsets of $\,{\cal N}=4\,$ theories happens not to be empty and, furthermore, contains some theories for which a realisation in terms of type IIA string theory is known.