Instantons and infinite distances

TL;DR

This work shows that in type II Calabi–Yau compactifications the classical infinite-distance geodesics in the hypermultiplet moduli space are dramatically altered by a tower of D-instantons with exponentially suppressed actions. Using the tensor (contact) potential, the authors derive the quantum-corrected metric along a large-volume, strong-coupling trajectory and demonstrate that the corrected distance becomes finite, while the 4d Planck mass and string scale adjust via a species-like mechanism. Through the c-map, these results connect to the vector multiplet sector and provide evidence for the Swampland Distance Conjecture and the Emergence Proposal in three dimensions, where a tower of light states generates the IR metric. The analysis also uncovers tensionless D-strings and imposes constraints on axion decay constants consistent with the weak gravity conjecture, suggesting a rich interplay between nonperturbative corrections, emergent physics, and swampland constraints in string compactifications.

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.