Quantum mirror symmetry and twistors

TL;DR

This paper employs the twistor approach to analyze hypermultiplet moduli spaces, deriving instanton contributions to the mirror map and revealing a quantum-correction-free SL(2,Z) action, with implications for resolving singularities.

Contribution

It introduces a novel twistor space description that clarifies instanton effects on the mirror map and the quantum corrections to the SL(2,Z) symmetry in string theory.

Findings

Derived instanton contributions to the mirror map.

Found SL(2,Z) action free from quantum corrections.

Discussed potential resolution of moduli space singularities.

Abstract

Using the twistor approach to hypermultiplet moduli spaces, we derive the worldsheet, D(-1), and D1-instanton contributions to the generalized mirror map, relating Type IIA and Type IIB string theory compactified on generic mirror Calabi-Yau threefolds. For this purpose, we provide a novel description of the twistor space underlying the Type IIB hypermultiplet moduli space where the SL(2,Z)-action is found to be free from quantum corrections. The extent to which instanton effects may resolve the perturbative singularities of the moduli space metric is discussed.