Hypermultiplet metric and NS5-instantons

TL;DR

This paper calculates explicit NS5-brane instanton corrections to the hypermultiplet moduli space metric in Calabi-Yau compactifications, providing new insights into non-perturbative effects in string theory.

Contribution

It derives all-order expressions for NS5-instanton corrections in the one-instanton approximation and verifies their consistency with known geometric descriptions.

Findings

Explicit formulas for NS5-instanton corrections

Verification of the metric's self-dual Einstein structure

Predictions for string amplitudes involving NS5-branes

Abstract

The metric on the hypermultiplet moduli space of Calabi-Yau compactifications of type II string theory is known to receive D-brane and NS5-brane instanton corrections. We compute explicit expressions for these corrections in the one-instanton approximation, but to all orders in the string coupling expansion around the instantons. As a consistency check, we prove that in the case of one (universal) hypermultiplet, the resulting metric fits the Przanowski description of self-dual Einstein spaces. We also show that in the small string coupling limit the metric acquires a certain square structure, consistently with expectations from the string amplitudes analysis. This result provides explicit predictions for yet mysterious string amplitudes in the presence of NS5-branes.