On the topology of the hypermultiplet moduli space in type II/CY string vacua

TL;DR

This paper investigates the topology of the hypermultiplet moduli space in type II Calabi-Yau string compactifications, revealing the role of NS5-brane instantons and the non-trivial fiber bundle structure of the Neveu-Schwarz axion.

Contribution

It identifies the topological structure of the hypermultiplet moduli space influenced by NS5-brane instantons and clarifies the axion's role as a fiber coordinate in a circle bundle.

Findings

Neveu-Schwarz axion parametrizes the fiber of a circle bundle.

Translations along the intermediate Jacobian induce non-trivial axion shifts.

The topology is consistent with fivebrane instanton effects.

Abstract

By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the Calabi-Yau metric. Specifically, we show that for fivebrane instanton couplings to be well-defined, translations along the intermediate Jacobian must induce non-trivial shifts of the Neveu-Schwarz axion which had thus far been overlooked. As a result, the Neveu-Schwarz axion parametrizes the fiber of a circle bundle, isomorphic to the one in which the fivebrane partition function is valued. In the companion paper arXiv:1010.5792, we go beyond the present analysis and take steps towards a quantitative description of fivebrane instanton corrections, using a combination of mirror symmetry, S-duality, topological string theory and twistor techniques.