MS Seminar (Mathematics - String Theory)

Speaker: Edgar Shaghoulian (UCSB)
Title: Modular forms, new Cardy formulas, and black hole entropy.
Date: Wed, Apr 13, 2016, 13:15 - 14:30
Place: Seminar Room B
Abstract: 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 new Cardy formulas which relate the asymptotic degeneracy of states with fixed charges to the vacuum energy. After a few checks of the formulas, we will use them to reproduce the Bekenstein-Hawking entropy of large AdS-Schwarzschild black holes (plus logarithmic corrections), boosted AdS-Schwarzschild black branes, and large AdS-Kerr black holes with arbitrary angular velocities. These calculations generalize Strominger's microscopic count of the BTZ black hole entropy to higher dimensions. If time permits, we will provide extensions of this framework to theories which violate hyperscaling and unitarity.