Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

Abstract

We calculate the Rényi entropy $S_q(\mu ,\lambda )$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings $\lambda$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\frac{\partial }{\partial q}\left(\frac{q-1}{q}{S}_q(\mu ,\lambda )\right)\ge 0$, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of $S_q(\mu ,\lambda )$ for imaginary chemical potential, between negative and non-negative $\lambda$.

50 pages, 16 figures. v3: Version to appear in JHEP

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• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• On the Rényi entropy of Lifshitz and hyperscaling violating black holes
• Shape Deformations of Charged Rényi Entropies from Holography