Speaker
Daniël Prins
(Lyon)
Description
The supersymmetry equations are a set of Killing spinor equations that determine supersymmetric flux vacua of type II supergravity. In certain cases for product manifolds R^{1, 9-2n} \times M_2n, these equations have been recast to resemble integrability conditions of generalized almost complex structures: in all such cases, M_2n can be equipped with an SU(n)-structure. This begs the question to what extent this equivalence holds when considering n=5. An obvious obstacle to overcome is that this can only work for Riemannian, rather than Lorentzian manifolds. I will demonstrate that, by making use of complex supergravity, one can show that a necessary but not quit sufficient condition for solutions to the supersymmetry equations on manifolds with SU(5)-structure can indeed be given in terms of generalized almost complex structures.
