Type II Strings and Generalized Calabi-Yau Manifolds
Abstract
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.
Cite
@article{arxiv.hep-th/0409176,
title = {Type II Strings and Generalized Calabi-Yau Manifolds},
author = {Mariana Graña and Ruben Minasian and Michela Petrini and Alessandro Tomasiello},
journal= {arXiv preprint arXiv:hep-th/0409176},
year = {2015}
}
Comments
9 pages, Proceedings of Strings 2004, Paris, June 28-July 2