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Supersymmetric backgrounds from generalized Calabi‐Yau manifolds
Author(s) -
Grana M.,
Minasian R.,
Petrinin M.,
Tomasiello A.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200410239
Subject(s) - calabi–yau manifold , symplectic geometry , holomorphic function , mirror symmetry , pure mathematics , supersymmetry , spinor , mathematical physics , hyperkähler manifold , physics , rank (graph theory) , effective action , ricci flat manifold , mathematics , action (physics) , scalar curvature , curvature , combinatorics , quantum mechanics , geometry
Abstract We show that the supersymmetry transformations for type II string theories onsix‐manifolds can be written as differential conditions on a pair of purespinors, the exponentiated Kähler form e iJ and the holomorphic formO. The equations are explicitly symmetric under exchange of thetwo pure spinors and a choice of even or odd‐rank RR field.This is mirror symmetry formanifolds with torsion. Moreover, RR fluxes affect only one of the twoequations: e iJ is closed under the action of the twisted exteriorderivative in IIA theory, and similarly O is closed in IIB. This means thatsupersymmetric SU(3)‐structure manifolds are always complex in IIB while they are twisted symplecticin IIA. Modulo adifferent action of the B ‐field, these are all generalized Calabi‐Yau manifolds, asdefined by Hitchin.