Mirror Symmetry in Generalized Calabi-Yau Compactifications

TL;DR

This paper explores mirror symmetry in generalized Calabi-Yau compactifications with NS fluxes, revealing that mirror pairs involve manifolds with SU(3) structure that are neither complex nor Ricci-flat, extending mirror symmetry beyond traditional Calabi-Yau spaces.

Contribution

It demonstrates that mirror symmetry in flux compactifications involves half-flat manifolds with SU(3) structure, broadening the understanding of mirror pairs in string theory.

Findings

Mirror type IIA arises from geometrical compactification on half-flat manifolds.

Half-flat manifolds have SU(3) structure but are neither complex nor Ricci-flat.

The low-energy effective action matches mirror symmetry expectations.

Abstract

We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are termed half-flat; they are neither complex nor Ricci-flat and their holonomy group is no longer SU(3). We show that type IIA appropriately compactified on such manifolds gives the correct mirror-symmetric low-energy effective action.