Topological mirror symmetry with fluxes

TL;DR

This paper constructs topological mirror pairs for Calabi-Yau manifolds with NS fluxes, revealing how fluxes correspond to torsion in the mirror's cohomology, advancing understanding of flux compactifications.

Contribution

It explicitly constructs half-flat topological mirrors to Calabi-Yau manifolds with fluxes, linking flux units with torsion factors and modifying SYZ fibrations.

Findings

Flux units are exchanged with torsion in the mirror's cohomology.

Explicit forms for Kaluza-Klein reduction are identified.

Formality indicates these forms carry no topological information.

Abstract

Motivated by SU(3) structure compactifications, we show explicitly how to construct half--flat topological mirrors to Calabi--Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential--geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi--Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza--Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.