D-instantons and twistors

TL;DR

This paper develops a geometric framework using twistor space to incorporate D-instanton effects into the hypermultiplet moduli space metric in Type II string theory, connecting instanton corrections to contact geometry and dilogarithm functions.

Contribution

It introduces a novel approach to encode D-instanton corrections via contact transformations in twistor space, unifying various effects and relating them to known mathematical structures.

Findings

Expressed D-instanton effects as sums of dilogarithm functions.

Recast known D2-instanton corrections in contact geometry language.

Connected instanton corrections to black hole degeneracies and wall-crossing phenomena.

Abstract

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.