# Instantons and infinite distances

## TL;DR

This paper studies the impact of D-instantons on the geometry of hypermultiplet moduli space in type II Calabi-Yau compactifications, revealing how instanton effects can render infinite distance paths finite and relate to swampland conjectures.

## Contribution

It demonstrates how instanton corrections modify the moduli space metric and dilaton behavior near infinite distance points, supporting the Swampland Distance Conjecture and Emergence Proposal.

## Key findings

- Instanton effects can make infinite geodesic distances finite.
- The corrected metric influences the string scale and Planck mass.
- Results support conjectures relating infinite distances to emergent physics.

## Abstract

We consider geodesics of infinite length and constant 4d dilaton in the (classical) hypermultiplet moduli space of type II Calabi-Yau compactifications. When approaching such infinite distance points, a large amount of D-instantons develop an exponentially suppressed action, substantially modifying the moduli space metric. We consider a particular large volume/strong coupling trajectory for which, in the corrected metric, the path length becomes finite. The instanton effects also modify the cllassical 4d dilaton such that, in order to keep the 4d Planck mass finite, the string scale has to be lowered. Our results can be related, via the c-map, to the physics around points of infinite distance in the vector multiplet moduli space where the Swampland Distance Conjecture and the Emergence Proposal have been discussed, and provide further evidence for them.