Abstract
Motivated by extended black hole thermodynamics, we generalize the Rényi entropy of charged holographic conformal field theories (CFTs) in d-dimensions. Specifically, following [], we extend the quench description of the Rényi entropy of globally charged holographic CFTs by including pressure variations of charged hyperbolically sliced anti de Sitter black holes. We provide an exhaustive analysis of the new type of charged Rényi entropy, where we find an interesting interplay between a parameter controlling the pressure of the black hole and its charge. A field theoretic interpretation of this extended charged Rényi entropy is given. In particular, in d = 2, where the bulk geometry becomes the charged Bañados, Teitelboim, Zanelli black hole, we write down the extended charged Rényi entropy in terms of the twist operators of the charged field theory. An area law prescription for the extended Rényi entropy is formulated. We comment on several avenues for future work, including how global charge conservation relates to black hole super-entropicity.
Highlights
When the field theory in question carries a conserved charge, the entanglement Renyi entropy Sq is replaced with a grand canonical version of (1.2), eμQA q
We have extended the charged holographic Renyi entropy Sq(μ) of a globally charged holographic conformal field theories (CFTs) characterized by a chemical potential μ
Our generalization was motivated by the extended black hole thermodynamics of charged AdS black holes with hyperbolically sliced horizons
Summary
When we consider quantum field theories with a conserved global charge, the Renyı entropy is generalized to a charged Renyi entropy, given in (1.3), where μ is a ‘chemical potential’ and QA is the charge confined to the subsystem of interest [11]. When the quantum field theory is a CFT, the charged Renyi entropy can be evaluated expressed using the quench (1.5), where the CHM map (1.4) generalizes to ρA eμQA = U −1 e−Hτ /T0+μQA U , ρtherm = e−Hτ /T0+μQA. This theory admits charged topological black holes with metric ds2 = −f (r)dτ 2 + f −1(r)dr2 + r2(du2 + sinh2(u)dΩ2d−2) ,. We emphasize by SEE we really mean the entanglement entropy for the neutral CFT, SEE(μ = 0) Charged Renyi entropies constructed from an imaginary chemical potential are of interest. This can be done on the field theory side by analytically continuing μ → iμE for μE real. The event horizon of the black hole disappears leaving a naked singularity
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