Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series

Abstract: The microscopic spectrum of half-BPS excitations in toroidally compactified heterotic string theory has been computed exactly through the use of results from analytic number theory. Recently, similar quantities have been understood macroscopically by evaluating the gravitational path integral on the M-theory lift of the AdS2 near-horizon geometry of the corresponding black hole. In this paper, we generalize these results to a subset of the CHL models, which include the standard compactification of IIA on $K3\times T^2$ as a special case. We begin by developing a Rademacher-like expansion for the Fourier coefficients of the partition functions for these theories, which are modular forms for congruence subgroups. We then interpret these results in a macroscopic setting by evaluating the path integral for the reduced-rank $\mathcal{N} = 4$ supergravities described by these CFTs.