Supersymmetric Rényi entropy and charged hyperbolic black holes

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 -d−1×S1, 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.