Seminar

Black hole microstate counting is one of the greatest successes of string theory. In particular, the 4d N=4 string vacuum obtained by compactifying type II on K3 x T^2 (or, dually, heterotic on T^6) has proved to be a Goldilocks case, as the theory is non-trivial (we do not even know a Calabi-Yau metric for any smooth K3 surface!), but sufficiently constrained that we can learn a lot about it. The automorphic form encoding its 1/4-BPS state counts has by now been computed via a variety of different methods, and the relationship between decays of BPS states at walls of marginal stability in moduli space and poles of this automorphic form has been elucidated. In this talk, I will review these results, and then explain how to generalize them to the other known examples of 4d N=4 string vacua, the CHL models, which are orbifolds of heterotic on T^6. In particular, I will explain the classification of these models in terms of the symmetries of K3 string theory, and I will explain how to determine their 1/4-BPS counting functions by using K3 string theory dualities and considerations from wall crossing. Time permitting, I will relate these BPS state counts to Umbral moonshine. (This talk is based on 1612.04404, 1702.05095, and possibly 1803.07567.)