Abstract
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 ℍd−1× \U0001d54a1, 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.
Highlights
The entanglement entropy of the vacuum is an example of a universal observable in quantum field theory, independent of the existence of a particular set of fields, which has many interesting and useful properties
We focus on the gravity duals to Supersymmetric Renyi entropy (SRE) in four and six dimensions, which are hyperbolic black holes
Following the work on magnetically charged AdS4 black holes in [64], intense efforts have been put into the holographic computation of entropy for BPS black holes with compact horizons, using localization
Summary
The entanglement entropy of the vacuum is an example of a universal observable in quantum field theory, independent of the existence of a particular set of fields, which has many interesting and useful properties. The matching with the gravity computation of the SRE was achieved with supergravity hyperbolic black holes supported by a single gauge field, which corresponds to the graviphoton. We take this one step further by considering supergravity backgrounds with more general couplings, in particular vector multiplets. We will first provide results for the supersymmetric Renyi entropy with flavor fugacities for specific models: the ABJM model in d = 3, and a N = 1, USp(2N ) gauge theory with Nf fundamental and one anti-symmetric hypermultiplets in d = 5 These models have well known gravity dual descriptions. In appendix D, we present a simple example of a rotating hyperbolic black hole which generalizes the static case in section 3.1, and provide the value of its renormalized on-shell action
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