Description
In this talk, I will discuss properties of the spectrum of charged states in theories of gravity with minimal supersymmetry arising as compactifications of M-/F- and string theory to 6-,5-, and 4-dimensions. According to the Weak Gravity Conjecture, the spectrum of charged states has to contain charged states for which the charge-to-mass ratio exceeds that of extremal black holes. In theories with minimal supersymmetry, explicit checks of this conjecture require considering states in the non-BPS secotr of the theory arising as excitations of strings. Exploiting the properties of the geometry of the compactification manifold, I will demonstrate that the full theory of quantum gravity contains exactly those states required to satisfy the weak gravity conjecture. In particular, using the modular properties of the elliptic genera of weakly coupled strings arising from wrapped branes, I will show that for gauge theories, which can become weakly coupled in quantum gravity, a full tower of super-extremal states exists, ensuring consistency of the Weak Gravity Conjecture under dimensional reduction.
