Mirror symmetric SU(3)-structure manifolds with NS fluxes

TL;DR

This paper explores mirror symmetry in string theory compactifications with NS fluxes, focusing on T^3-fibered SU(3)-structure manifolds and the exchange of geometric and flux data under T-duality.

Contribution

It introduces a framework for understanding mirror symmetry with NS fluxes in T^3-fibered geometries, extending to generic cases via twisted covariant derivatives.

Findings

Exchange of pure spinors under T-duality.

Transformation rules for NS flux and intrinsic torsion.

Proposal for mirror symmetry in flux compactifications.

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 \Omega) 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.