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 exp(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: exp(iJ) is closed under the action of the twisted exterior derivative in IIA theory, and similarly Omega is closed in IIB. Modulo a different action of the B-field, this means that supersymmetric SU(3)-structure manifolds are all generalized Calabi-Yau manifolds, as defined by Hitchin. An equivalent, and somewhat more conventional, description is given as a set of relations between the components of intrinsic torsions modified by the NS flux and the Clifford products of RR fluxes with pure spinors, allowing for a classification of type II supersymmetric vacua on six-manifolds. We find in particular that supersymmetric six-manifolds are always complex for IIB backgrounds while they are twisted symplectic for IIA.

Grana, M., Minasian, R., Petrini, M., Tomasiello, A. (2004). Supersymmetric backgrounds from generalized Calabi-Yau manifolds. JOURNAL OF HIGH ENERGY PHYSICS, 8(8), 1229-1262 [10.1088/1126-6708/2004/08/046].

Supersymmetric backgrounds from generalized Calabi-Yau manifolds

TOMASIELLO, ALESSANDRO
2004

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 Kahler form exp(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: exp(iJ) is closed under the action of the twisted exterior derivative in IIA theory, and similarly Omega is closed in IIB. Modulo a different action of the B-field, this means that supersymmetric SU(3)-structure manifolds are all generalized Calabi-Yau manifolds, as defined by Hitchin. An equivalent, and somewhat more conventional, description is given as a set of relations between the components of intrinsic torsions modified by the NS flux and the Clifford products of RR fluxes with pure spinors, allowing for a classification of type II supersymmetric vacua on six-manifolds. We find in particular that supersymmetric six-manifolds are always complex for IIB backgrounds while they are twisted symplectic for IIA.
Articolo in rivista - Articolo scientifico
teoria di stringa; compattificazioni
English
2004
8
8
1229
1262
none
Grana, M., Minasian, R., Petrini, M., Tomasiello, A. (2004). Supersymmetric backgrounds from generalized Calabi-Yau manifolds. JOURNAL OF HIGH ENERGY PHYSICS, 8(8), 1229-1262 [10.1088/1126-6708/2004/08/046].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/12704
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