Non-Kaehler SYZ mirror symmetry
Siu-Cheong Lau, Li-Sheng Tseng, Shing-Tung Yau
TL;DR
This paper explores SYZ mirror symmetry for non-Kaehler Calabi-Yau manifolds, demonstrating that Fourier-Mukai transform acts as the mirror map in semi-flat settings, especially on nilmanifolds.
Contribution
It generalizes SYZ mirror symmetry to non-Kaehler contexts and shows Fourier-Mukai transform as the mirror map for these systems.
Findings
Fourier-Mukai transform provides the mirror map in non-Kaehler settings
Mirror symmetry extends to higher-dimensional non-Kaehler Calabi-Yau manifolds
Nilmanifolds serve as concrete examples for the theory
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 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.
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