Paolo Benincasa, Niels Bohr Institute
Understanding $\operatorname{AdS}_2$: From Calogero-like models and SLE to $4d$ black hole microstate entropy

Extremal black holes show the presence of an $\operatorname{AdS}_2$ factor as an universal feature. This fact provides a strong motivation for getting a deeper understanding of $\operatorname{AdS}_2$ spacetimes. In this talk, I will argue how $\operatorname{AdS}_2$ systems have a natural description in terms of $1d$ Calogero-type models and, in turn to SLE curves, which describe the geodesic motion of particles in $\operatorname{AdS}_2$. This treatment allows to compute the dimension of the phase space of these geodesics, linking it to the leading Bekenstein-Hawking black hole entropy and the black hole degeneracy.