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

TL;DR

The paper determines the global topology of the hypermultiplet moduli space $\mathcal{M}_H$ in type II Calabi–Yau vacua by enforcing the consistency of NS5-brane instanton couplings, showing that the Neveu–Schwarz axion $\sigma$ fibers a circle bundle whose holonomies are tied to the fivebrane partition function. It demonstrates that large gauge transformations act with a nontrivial shift $2c(H)$ in $\sigma$, yielding a modified Heisenberg-like symmetry group and leading to the natural identification of the NS-axion circle bundle with the fivebrane bundle over the intermediate Jacobian. The analysis also links the NS-axion bundle topology to the D-instanton sector by arguing that the NS5 and D5 quadratic refinements must coincide ($\Theta=\Theta_D$) for consistency under monodromies and S-duality. Furthermore, the work shows that the curvature of the NS-axion bundle over the complex structure moduli space involves the Hodge line bundle, highlighting subtleties in defining monodromy transformations and indicating the need for determinant line bundles in a complete global formulation. These results establish a concrete geometric framework for incorporating fivebrane instanton corrections and set the stage for a quantitative treatment in the companion paper.

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.