Supersymmetric backgrounds from generalized Calabi-Yau manifolds

✍ Scribed by M. Grana; R. Minasian; M. Petrinin; A. Tomasiello

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 140 KB
• Volume: 53
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200410239

✦ Synopsis

Abstract

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 Kähler form e^iJ^ and the holomorphic form
O. 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 O 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.