Generalized Calabi-Yau structures and mirror symmetry

Abstract

We use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown that not only the metric and B-field but also the algebraic structures are uniquely mapped. As an example we use the six-torus as a trivial generalized Calabi-Yau 6-fold and an appropriate B-field.

AMS-LaTeX, 15 pages, no figures; v2: typos corrected, citations clarified

References in corpus (4)

• Topological strings on noncommutative manifolds
• Mirror symmetric SU(3)-structure manifolds with NS fluxes
• Mirror Symmetry and Generalized Complex Manifolds
• O(d,d;R) Deformations of Complex Structures and Extended Worldsheet Supersymmetry

Cited by in corpus (12)

• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• Lectures on Generalized Complex Geometry for Physicists
• Gauged Supergravities
• The Hitchin functionals and the topological B-model at one loop
• Generalized complex geometry, generalized branes and the Hitchin sigma model
• N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures
• Conifolds and Geometric Transitions
• Calibrated cycles and T-duality
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Twistor spaces of generalized complex structures
• Study of the OSV Conjecture for 4D N=2 Extremal Black Holes in Type IIB String Theory