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

Abstract

We consider = (2,0) backgrounds of IIB supergravity on eight-manifolds ℳ8 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 ℳ8. One consequence of supersymmetry is that ℳ8 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. We identify the missing constraints and express them in the form of a single pure-spinor equation which is well defined for generic SU(4) × SU(4) backgrounds. This additional equation is given in terms of a certain analytic continuation of the generalized calibration form for codimension-2 static, magnetic D-branes. © 2013 SISSA.