IIB supergravity on manifolds with SU(4) structure and generalized geometry

Understand

We consider N=(2,0) backgrounds of IIB supergravity on eight-manifolds M_8 with strict SU(4) structure.

• We give the explicit solution to the Killing spinor equations as a set of algebraic relations between irreducible su(4) modules of the fluxes and the torsion classes of M_8.
• One consequence of supersymmetry is that M_8 must be complex.
• We show that the conjecture of arxiv:1010.5789 concerning the correspondence between background supersymmetry equations in terms of generalized pure spinors and generalized calibrations for admissible static, magnetic D-branes, does not capture the full set of supersymmetry equations.