Supersymmetric sources, integrability and generalized-structure compactifications

TL;DR

This paper explores supersymmetric compactifications with generalized structures, demonstrating compatibility with orientifold sources and proving integrability of equations of motion under certain conditions, with explicit examples and new calibration forms.

Contribution

It shows orientifold sources can be compatible with generalized SU(3) x SU(3)-structures and proves integrability of equations of motion in these backgrounds, including explicit T-dual examples.

Findings

Orientifold sources compatible with generalized SU(3) x SU(3)-structure.

Source-corrected equations of motion follow from supersymmetry and form equations.

Calibration form for space-filling NS5-brane obtained.

Abstract

In the context of supersymmetric compactifications of type II supergravity to four dimensions, we show that orientifold sources can be compatible with a generalized SU(3) x SU(3)-structure that is neither strictly SU(3) nor static SU(2). We illustrate this with explicit examples, obtained by suitably T-dualizing known solutions on the six-torus. In addition we prove the following integrability statements, valid under certain mild assumptions: (a) for general type II supergravity backgrounds with orientifold and/or D-brane generalized-calibrated sources, the source-corrected Einstein and dilaton equations of motion follow automatically from the supersymmetry equations once the likewise source-corrected form equations of motion and Bianchi identities are imposed; (b) in the special case of supersymmetric compactifications to four-dimensional Minkowski space, the equations of motion of all fields, including the NSNS three-form, follow automatically once the supersymmetry and the Bianchi identities of the forms are imposed. Both (a) and (b) are equally valid whether the sources are smeared or localized. As a byproduct we obtain the calibration form for a space-filling NS5-brane.