Hypermultiplets and Topological Strings

TL;DR

This paper develops a superspace framework linking hypermultiplet moduli spaces in string theory to topological string computations, enabling analysis of quantum corrections and black hole wave-functions.

Contribution

It provides an off-shell superspace description of the c-map, connecting hypermultiplet Lagrangians to topological string theory calculations.

Findings

Superspace Lagrangian for hypermultiplets related to the prepotential.

Higher derivative terms computed from higher genus topological string amplitudes.

Framework for quantum corrections to hypermultiplet moduli space.

Abstract

The c-map relates classical hypermultiplet moduli spaces in compactifications of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces via a further compactification on a circle. We give an off-shell description of the c-map in N=2 superspace. The superspace Lagrangian for the hypermultiplets is a single function directly related to the prepotential of special geometry, and can therefore be computed using topological string theory. Similarly, a class of higher derivative terms for hypermultiplets can be computed from the higher genus topological string amplitudes. Our results provide a framework for studying quantum corrections to the hypermultiplet moduli space, as well as for understanding the black hole wave-function as a function of the hypermultiplet moduli.