Rigid limit for hypermultiplets and five-dimensional gauge theories

TL;DR

This paper investigates the rigid limit of hypermultiplet moduli spaces in Calabi-Yau compactifications, revealing a hyperkahler quotient structure and connecting it to five-dimensional gauge theories and instanton effects.

Contribution

It introduces a new geometric construction of the hypermultiplet moduli space in the rigid limit using hyperkahler quotients, linking string theory results to gauge theory instantons.

Findings

Derived the hyperkahler metric including all D-instanton corrections.

Established a condition for the existence of a local limit based on Calabi-Yau intersection numbers.

Connected the hypermultiplet moduli space to five-dimensional gauge theories on a torus.

Abstract

We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is obtained by performing a hyperkahler quotient of the Swann bundle over the moduli space, along the isometries arising in the limit. Physically, this manifold appears as the target space of the non-linear sigma model obtained by compactification of a five-dimensional gauge theory on a torus. This allows to compute dyonic and stringy instantons of the gauge theory from the known results on D-instantons in string theory. Besides, we formulate a simple condition on the existence of a non-trivial local limit in terms of intersection numbers of the Calabi-Yau, and find an explicit form for the hypermultiplet metric including corrections from all mutually non-local D-instantons, which can be of independent interest.