Tensionless strings and the weak gravity conjecture

We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. We show that such a limit must be located at infinite distance in the moduli space. As expected, the low-energy effective theory breaks down in this limit due to a tower of charged particles becoming massless. These are the excitations of an asymptotically tensionless string, which is shown to coincide with a critical heterotic string compactified to six dimensions.