Twistor Approach to String Compactifications: a Review

TL;DR

This review discusses how the twistor approach effectively captures non-perturbative quantum corrections, including instantons, in the hypermultiplet moduli space of type II string compactifications on Calabi-Yau manifolds, revealing deep geometric and duality insights.

Contribution

It demonstrates the incorporation of all quantum corrections into the twistor framework, advancing understanding of string compactifications and related dualities.

Findings

Unified description of quantum corrections via twistor methods

Insights into S-duality and quantum mirror symmetry

Connections established with integrable models and topological strings

Abstract

We review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the hypermultiplet moduli space. We show how all these corrections, which include D-brane and NS5-brane instantons, are incorporated in the framework of the twistor approach, which provides a powerful mathematical description of hyperkahler and quaternion-Kahler manifolds. We also present new insights on S-duality, quantum mirror symmetry, connections to integrable models and topological strings.