Modularity, Quaternion-Kahler spaces and Mirror Symmetry

TL;DR

This paper develops a twistorial method to construct quaternion-Kahler manifolds with modular symmetry, providing a comprehensive non-perturbative mirror map relevant for string theory compactifications.

Contribution

It introduces a general twistorial framework for quaternion-Kahler spaces with SL(2,Z) symmetry, capturing NS5-brane instanton effects without continuous isometries.

Findings

Explicit twistorial construction of modular-invariant quaternion-Kahler manifolds

Complete non-perturbative mirror map between type IIA and IIB fields

Framework applicable to string compactifications with N=2 supersymmetry

Abstract

We provide an explicit twistorial construction of quaternion-Kahler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and therefore this construction presents a general framework for describing NS5-brane instanton effects in string compactifications with N=2 supersymmetry. In this context the modular invariant parametrization of twistor lines found in this work yields the complete non-perturbative mirror map between type IIA and type IIB physical fields.