We test various conjectures on quantum gravity for general 6d string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we first analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. A key observation is made about the appearance of a tensionless string in such a limit. For a more quantitative analysis, we focus on a U(1) gauge symmetry and determine the elliptic genus of this string in terms of certain meromorphic weak Jacobi forms, of which modular properties allow us to determine the charge-to-mass ratios of certain string excitations. A tower of these asymptotically massless charged states are then confirmed to satisfy the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. If time permits, we interpret their charge-to-mass ratios in two a priori independent perspectives. All of this is then generalized to theories with multiple U(1)s.
- String Theory Seminar