Spectra of BPS Strings in 6d Supergravity and the Swampland

TL;DR

This paper develops a modular approach to compute elliptic genera of BPS strings in 6d supergravity, validating Swampland conjectures and exploring non-geometric theories with tensionless strings.

Contribution

It introduces a novel modular ansatz for elliptic genera, applies mirror symmetry for validation, and extends the analysis to non-geometric theories confirming key Swampland conjectures.

Findings

Validated the modular ansatz for elliptic genera.

Confirmed Swampland conjectures in non-geometric 6d theories.

Identified tensionless little strings near infinite-distance limits.

Abstract

We explore BPS strings in supergravity theories in six-dimensions and related Swampland Conjectures. We first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d theories. By employing mirror symmetry on F-theory examples, we explicitly compute the elliptic genera and validate our ansatz. We extend this approach to investigate BPS strings and their spectrum in non-geometric 6d theories which have no known F-theory constructions, and confirm the Swampland conjectures, including the Weak Gravity Conjecture, Distance Conjecture, and Emergent String Conjecture. We also discuss tensionless little strings that emerge near infinite-distance limits of strong gauge coupling in the moduli space of certain special theories.