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We perform a holographic calculation of the Entanglement Renyi entropy Sq(m;l), for spherical entangling surfaces in boundary CFT’s with Einstein-Gauss-Bonnet-Maxwell holographic gravitational duals. We find that for Gauss-Bonnet couplings l , larger than a specific value, but still allowed by causality, a violation of an inequality that Renyi entropies must obey by definition occurs. This violation is related to the existence of negative entropy black holes and restricts the coefficient of the Gauss-Bonnet coupling in the bulk theory. Furthermore, we discover a distinction in the analytic structure of the analytic continuation of Sq(m;l), between negative and non-negative l , suggesting the existence of a phase transition.

Holographic Calculation of Renyi Entropies and Restrictions on Higher Derivative Terms