Ever since the seminal work by Strominger and Vafa, the black hole entropy can be computed by applying the Cardy formula to some 2d CFT. In the last few years, the AdS/CFT correspondence was found to be able to produce the AdS black hole entropy. Initially, the Cardy formula does not play a role in this new picture. However, we will demonstrate in this talk that the AdS black hole entropy can also be obtained from the two-dimensional Cardy formula and its higher-dimensional counterpart. In particular, despite the absence of conformal anomaly in odd dimensions, we generalize the even-dimensional Cardy-like formulae found by Komargodski et al. to odd dimensions and compute the BPS AdS_4 black hole entropy from a 3d Cardy-like formula. This talk is based on 2005.10251 and an upcoming paper.

Contact: Wu Jieqiang