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

TL;DR

This paper analyzes N=(2,0) IIB supergravity backgrounds on eight-manifolds with SU(4) structure, providing explicit solutions to Killing spinor equations, and clarifies the relationship between supersymmetry conditions and generalized calibrations.

Contribution

It explicitly solves the Killing spinor equations for SU(4) structured manifolds and identifies missing supersymmetry constraints not captured by previous conjectures.

Findings

M_8 must be a complex manifold.

The conjecture relating supersymmetry equations to generalized calibrations is incomplete.

A new pure-spinor equation captures the full set of supersymmetry conditions.

Abstract

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. 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)\times 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.