Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes

Abstract

When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T 3 -fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e iJ and Ω) in dual geometries under fiberwise T-duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.

Complex/Symplectic Mirrors

“…(Evidence so far includes mathematical insight [2], and, in the slightly more general context of SU(3) structure manifolds, comparisons of four-dimensional theories [32,33] and direct SYZ computation [34].) Suppose now we start (in the IIA theory) with a symplectic manifold W (whose moduli space is, as we said, modeled on H 2 (M, R)), and that for some value of the symplectic moduli some curves shrink.…”

Non-Kähler SYZ Mirror Symmetry

“…T-duality and SYZ in the setting of generalized Calabi-Yau manifolds were studied in [BEM04,BHM04,FMT05,GSN07,CG10] where H-flux played the key role, and also from the bispinor perspective which includes RR fluxes in [GMPT07,GMPW09]. The emphasis of this paper is different: we study SYZ in the presence of RR-flux and in particular focusing on the balanced Hermitian metric condition on non-Kähler manifolds, which also appears as part of the Strominger system [Str86].…”

Supersymmetric backgrounds from generalized Calabi–Yau manifolds

“…The issue of extending mirror symmetry to compactifications with fluxes has been studied recently in [1][2][3][4]. A first question is of course within which class of manifolds this symmetry should be defined.…”