Abstract
We prove a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges. This sharpens our previous analysis by including massless scalar fields. The latter are known to modify the Weak Gravity Conjecture bound in two a priori independent ways: First, the extremality condition of a charged black hole is modified, and second, the test particles required to satisfy the Weak Gravity Conjecture are subject to additional Yukawa type interactions. We argue on general grounds that at weak coupling, the two types of effects are equivalent for a tower of asymptotically massless charged test particles predicted by the Swampland Distance Conjecture.We then specialize to F-theory compactified on elliptic Calabi–Yau three-folds and prove that the precise numerical bound on the charge-to-mass ratio is satisfied at weak coupling. This amounts to an intriguing coincidence of two a priori different notions of extremality, namely one based on the balance of gauge, gravitational and scalar forces for extremal (non-BPS) black holes, and the other encoded in the modular properties of certain Jacobi forms. In the presence of multiple abelian gauge group factors, the elliptic genus counting these states is a lattice quasi-Jacobi form of higher rank, and we exemplify this in a model with two abelian gauge group factors.
Highlights
Introduction and summaryIn a consistent quantum theory, the gravitational and the non-gravitational sectors are typically far from independent
The latter are known to modify the Weak Gravity Conjecture bound in two a priori independent ways: First, the extremality condition of a charged black hole is modified, and second, the test particles required to satisfy the Weak Gravity Conjecture are subject to additional Yukawa type interactions
We argue on general grounds that at weak coupling, the two types of effects are equivalent for a tower of asymptotically massless charged test particles predicted by the Swampland Distance Conjecture
Summary
In a consistent quantum theory, the gravitational and the non-gravitational sectors are typically far from independent. A number of remarkable conjectures constrain the properties of quantum field theories by requiring that they can be consistently coupled to quantum gravity. From a more applied point of view, its generalization to p-form interactions for p = 0 constrains theories of large field inflation, as reflected in a substantial corpus of work including [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] (for additional aspects of this axionic Weak Gravity Conjecture see [39,40,41]); other versions affect the allowed range of Stückelberg masses [38] and have been argued to have implications on neutrino physics [15,42,43] or the electroweak scale [44,45,46]. A lot of evidence for the various forms of the conjecture has already been accumulated in a string theoretic context e.g. in [1,4,11], in situations with extended supersymmetry in various numbers of dimensions
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