Informal High Energy Theory Seminar
A Holographic Perspective on the Weak Gravity Conjecture
The Weak Gravity Conjecture demands the existence of superextremal states in any weakly coupled gauge theory including gravity. Some of its variants can constrain significantly the allowed effective field theories of inflation/relaxation. The original argument suggests that these particles must exist in order to allow charged black holes to decay, but it is difficult to make it precise. I will take another route and describe a holographic proof of a (sub)lattice version of the WGC for compact gauge fields in AdS_3, using modular invariance of the dual CFT. In this case, only a sublattice of the full charge lattice presents superextremal states. This can be related to the presence of discrete gauge symmetries in the low-energy effective field theory. I will also comment on the case of 0-form gauge fields in AdS_3, which is perhaps more relevant to inflation EFTs. Finally, I will describe a route which will hopefully lead to a proof of the WGC in higher dimensions.