Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces

TL;DR

This work advances the understanding of NS5-brane instanton corrections to the hypermultiplet moduli space in type II string theory on Calabi–Yau threefolds by developing a twistorial, duality-consistent framework. It shows that NS5 effects are governed by non-Gaussian theta series whose weak-coupling limit reduces to the topological A- and B-model wave functions, and that mirror symmetry and S-duality link NS5 corrections in IIA and IIB pictures. A central result is the construction of twistorial data H^{(k)}_{\rm NS5} encoding (p,k)-fivebrane corrections, whose Penrose transform yields a non-Gaussian NS5 partition function that reduces to the Gaussian flux partition function with a one-loop B-model normalization at zero coupling. The topology of the HM moduli space is clarified: fivebrane corrections lift NS-axion translations, producing a twisted circle bundle over the intermediate Jacobian, with curvature containing contributions from both torus and moduli-space sectors and monodromy-induced shifts tied to charge quantization. Collectively, the results illuminate how D- and NS5-instantons intertwine with topological string amplitudes and DT invariants, offering a coherent nonperturbative picture and exposing subtle issues (phases, monodromy, Heisenberg action) that remain targets for future refinement.

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.