Gopakumar-Vafa Invariants and the Emergent String Conjecture

TL;DR

This paper investigates the Emergent String Conjecture within 5d supergravity from M-theory on Calabi-Yau threefolds, using Gopakumar-Vafa invariants to analyze gauge couplings and BPS spectra, supporting the conjecture's validity.

Contribution

It provides evidence for the Emergent String Conjecture by analyzing geometric and physical properties of Calabi-Yau threefolds, including a testable geometric consequence.

Findings

The conjecture holds for all complete intersection Calabi-Yau threefolds in products of projective spaces.

Gopakumar-Vafa invariants encode BPS spectra consistent with the conjecture.

A geometric consequence of the conjecture is verified in studied examples.

Abstract

The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every infinite-distance limit in the moduli space of a quantum gravity represents either a decompactification limit or an emergent string limit in some duality frame. Within the context of 5d supergravities coming from M-theory compactifications on Calabi-Yau threefolds, we find evidence for this conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which is encoded in the Gopakumar-Vafa invariants of the threefold. In the process, we disuss a testable geometric consequence of the Emergent String Conjecture, and we verify that it is satisfied in all complete intersection Calabi-Yau threefolds in products of projective spaces (CICYs).