Theory HEP Seminar

Modular forms and black hole entropy

Edgar Shaghoulian

UCSB

We will utilize modular invariance of (d+1)-dimensional conformal field theories to argue that the logarithm of the partition function transforms as the absolute value of a modular form of weight d-1. We will use this property to derive a generalized Cardy formula which relates the asymptotic degeneracy of states to the vacuum energy of the theory. After a few checks of the formula, we will use it to reproduce the Bekenstein-Hawking entropy of large AdS-Schwarzschild black holes, boosted AdS-Schwarzschild black branes, and large AdS-Kerr black holes with arbitrary angular velocities. This provides a precise microscopic accounting for the states of a large class of higher-dimensional black holes. If time permits, we will provide extensions of this framework to theories which violate hyperscaling