Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces

TL;DR

This paper studies quantum corrections from fivebrane instantons to the hypermultiplet moduli space in Calabi-Yau compactifications, revealing new topological and duality-related structures and their relation to topological string theories.

Contribution

It determines the topology of the hypermultiplet moduli space considering instanton effects and computes fivebrane instanton corrections using S-duality, linking them to topological string amplitudes.

Findings

Topological structure of the moduli space at fixed coupling clarified.

Fivebrane instanton corrections expressed as non-Gaussian theta series.

New insights into charge quantization and duality actions on moduli space.

Abstract

We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and NS5-instanton corrections, we determine the topology of the hypermultiplet moduli space at fixed string coupling, as previewed in arXiv:1009.3026. On the type IIB side, we compute corrections from (p,k)-fivebrane instantons to the metric on M (specifically, the correction to the complex contact structure on its twistor space Z) by applying S-duality to the D-instanton sum. For fixed fivebrane charge k, the corrections can be written as a non-Gaussian theta series, whose summand for k=1 reduces to the topological A-model amplitude. By mirror symmetry, instanton corrections induced from the chiral type IIA NS5-brane are similarly governed by the wave function of the topological B-model. In the course of this investigation we clarify charge quantization for coherent sheaves and find hitherto unnoticed corrections to the Heisenberg, monodromy and S-duality actions on M, as well as to the mirror map for Ramond-Ramond fields and D-brane charges.