Charged R\'enyi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

Understand

We calculate the R\'enyi entropy $S_q(\mu,\lambda)$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals.

• R\'enyi 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 $\lambda$.