Non-Kaehler SYZ mirror symmetry

Abstract

We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric $SU(3)$ systems with Ramond-Ramond fluxes, and generalize them to higher dimensions. We show that Fourier-Mukai transform provides the mirror map between these Type IIA and Type IIB supersymmetric systems in the semi-flat setting. This is concretely exhibited by nilmanifolds.

24 pages

References in corpus (6)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• T-duality for principal torus bundles
• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• IIB supergravity on manifolds with SU(4) structure and generalized geometry
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• Generalized geometry of two-dimensional vacua

Cited by in corpus (13)

• New supersymmetric vacua on solvmanifolds
• Anomaly Flow and T-Duality
• Stable Forms, Vector Cross Products and Their Applications in Geometry
• Special Lagrangian cycles and Calabi-Yau transitions
• Generalized geometry lectures on type II backgrounds
• Homogeneous symplectic half-flat 6-manifolds
• On the automorphism group of a symplectic half-flat 6-manifold
• The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds
• Non-Kähler Mirror Symmetry of the Iwasawa Manifold
• Higher dimensional generalizations of twistor spaces
• Mirror symmetry & supersymmetry on SU(4)-structure backgrounds
• $T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory
• SYZ mirror symmetry of solvmanifolds