The Weak Gravity Conjecture and BPS Particles. Issue 11 (29th September 2021)

• Record Type: Journal Article
• Authors: Alim, Murad; Heidenreich, Ben; Rudelius, Tom
• Is Part Of: Fortschritte der Physik. Volume 69:Issue 11/12(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-09-29
• Subjects: Calabi‐Yau manifolds -- M‐theory -- quantum gravity -- swampland -- weak gravity conjecture; Physics -- Periodicals; 530.05
• DOI: 10.1002/prop.202100125
• Languages: English
• ISSNs: 0015-8208

Abstract

Abstract: Motivated by the Weak Gravity Conjecture, we uncover an intricate interplay between black holes, BPS particle counting, and Calabi‐Yau geometry in five dimensions. In particular, we point out that extremal BPS black holes exist only in certain directions in the charge lattice, and we argue that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi‐Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the existence of infinite towers of holomorphic curves in every direction within the dual of the cone of effective divisors. We verify these geometric conjectures in a number of examples by computing Gopakumar‐Vafa invariants. Abstract : Motivated by the Weak Gravity Conjecture, an intricate interplay between black holes, BPS particle counting, and Calabi‐Yau geometry in five dimensions will be uncovered. In particular, it is pointed out that extremal BPS black holes exist only in certain directions in the charge lattice. It is argued that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi‐Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the existence of infinite towers of holomorphic curves in every direction within the dual of the cone of effective divisors. These geometric conjectures are verified in a number of examples by computing Gopakumar‐Vafa invariants.