Half-maximal supersymmetry from exceptional field theory

Abstract

We study $D\ge 4$-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal ${\mathrm{Minkowski}}_D$ and ${\mathrm{AdS}}_D$ vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised $\mathrm{SO}(d-1-N)$ structures, where $d=11-D$, and $N$ is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all $D\ge 4$ half-maximal warped ${\mathrm{AdS}}_D$ and Minkowski${}_D$ vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new $\mathrm{SO}(5,N)$ double field theory with a $(6+N)$-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional $\mathcal{N}=1$ supergravity and another yielding six-dimensional $\mathcal{N}=\left(2,0\right)$ SUGRA.

105 pages; v2: Added a section proving consistency of truncation at the level of the equations of motion, and some references; v3: Published version, minor typos corrected

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• Ten-dimensional origin of Minkowski vacua in $\mathcal{N}=8$ supergravity
• Locally non-geometric fluxes and missing momenta in M-theory
• Supersymmetric AdS backgrounds and weak generalised holonomy
• $\eta$-symbols in exceptional field theory