Supersymmetric Rényi entropy and charged hyperbolic black holes
Seyed Morteza Hosseini, Chiara Toldo, Itamar Yaakov
Abstract
A bstract The supersymmetric Rényi entropy across a spherical entangling surface in a d -dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on ℍ d− 1 × 𝕊 1 , which can be computed exactly using localization. We consider the holographically dual BPS solutions in ( d + 1)-dimensional matter coupled supergravity ( d = 3 , 5), which are charged hyperbolically sliced AdS black holes. We compute the renormalized on-shell action and the holographic supersymmetric Rényi entropy and show a perfect match with the field theory side. Our setup allows a direct map between the chemical potentials for the global symmetries of the field theories and those of the gravity solutions. We also discuss a simple case where angular momentum is added.