Type II Strings and Generalized Calabi-Yau Manifolds

Details Type II Strings and Generalized Calabi-Yau Manifolds Type II Strings and Generalized Calabi-Yau Manifolds

2004-09-17

arxiv.org/abs/hep-th/0409176v1

Comptes Rendus Physique 5 (2004) 979-986

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, Proceedings of Strings 2004, Paris, June 28-July 2

Scientific paper

This is a short version of hep-th/0406137. We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form e^{iJ} and the holomorphic form Omega. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: e^{iJ} is closed under the action of the twisted exterior derivative in IIA theory, and similarly Omega is closed in IIB. This means that supersymmetric SU(3)-structure manifolds are always complex in IIB while they are twisted symplectic in IIA. Modulo a different action of the B-field, these are all generalized Calabi-Yau manifolds, as defined by Hitchin.

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