Membrane and fivebrane instantons from quaternionic geometry

TL;DR

This paper computes one-instanton corrections to the hypermultiplet moduli space in string theory, using quaternionic geometry, providing explicit solutions that match supergravity results in the semi-classical limit.

Contribution

It introduces a method to encode instanton corrections via a single function in quaternion-Kahler geometry, including all fluctuations to all orders.

Findings

Explicit solutions for instanton corrections are provided.

Results agree with supergravity calculations in the semi-classical limit.

The approach encodes corrections in a single quaternionic function.

Abstract

We determine the one-instanton corrections to the universal hypermultiplet moduli space coming both from Euclidean membranes and NS-fivebranes wrapping the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely encoded by a single function characterizing a generic four-dimensional quaternion-Kahler metric without isometries. We give explicit solutions for this function describing all one-instanton corrections, including the fluctuations around the instanton to all orders in the string coupling constant. In the semi-classical limit these results are in perfect agreement with previous supergravity calculations.