Supersymmetric geometries of IIA supergravity I

Abstract

IIA supergravity backgrounds preserving one supersymmetry locally admit four types of Killing spinors distinguished by the orbits of $Spin(9,1)$ on the space of spinors. We solve the Killing spinor equations of IIA supergravity with and without cosmological constant for Killing spinors representing two of these orbits, with isotropy groups $Spin(7)$ and $Spin(7)⋉{\mathbb{R}}^8$. In both cases, we identify the geometry of spacetime and express the fluxes in terms of the geometry. We find that the geometric constraints of backgrounds with a $Spin(7)⋉{\mathbb{R}}^8$ invariant Killing spinor are identical to those found for heterotic backgrounds preserving one supersymmetry.

21 pages

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• Supersymmetric geometries of IIA supergravity II
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