Type IIB Theory on Half-flat Manifolds

TL;DR

This paper tests the mirror symmetry of NS fluxes by showing that Type IIB string theory compactified on half-flat SU(3) structure manifolds yields the same four-dimensional N=2 effective action as Type IIA theory compactified on Calabi–Yau three-folds with NS flux. The authors implement a KK reduction of Type IIB on a half-flat manifold, including non-harmonic basis expansions and the self-duality constraint for the five-form, and demonstrate that after dualization and field redefinitions the resulting action matches the Type IIA NS-flux action (up to the mirror-exchange of gauge-coupling data). The analysis confirms that half-flat manifolds serve as mirror partners to CY spaces with NS fluxes and clarifies how flux parameters map under mirror symmetry, while highlighting the need for an additional flux component to account for all NS flux degrees of freedom. The work also discusses the role of the Ferrara–Sabharwal (FeS) quaternionic metric for hypermultiplets and raises open questions about magnetic NS fluxes in this duality framework.

Abstract

In this note we derive the low-energy effective action of type IIB theory compactified on half-flat manifolds and we show that this precisely coincides with the low-energy effective action of type IIA theory compactified on a Calabi-Yau manifold in the presence of NS three-form fluxes. We provide in this way a further check of the recently formulated conjecture that half-flat manifolds appear as mirror partners of Calabi-Yau manifolds when NS fluxes are turned on.