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We construct a new class of entanglement measures by extending the usual definition of Renyi entropy to include a chemical potential. These charged Renyi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFTs with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Renyi entropies in free field theories.
Quantum Renyi relative entropies provide a one-parameter family of distances between density matrices, which generalizes the relative entropy and the fidelity. We study these measures for renormalization group flows in quantum field theory. We derive
We holographically compute the Renyi relative divergence $D_{alpha} (rho_{+} || rho_{-})$ between two density matrices $rho_{+}, ; rho_{-}$ prepared by path integrals with constant background fields $lambda_{pm}$ coupled to a marginal operator in JT
We compute genus two partition functions in two dimensional conformal field theories at large central charge, focusing on surfaces that give the third Renyi entropy of two intervals. We compute this for generalized free theories and for symmetric orb
An alternative method is presented for extracting the von Neumann entropy $-operatorname{Tr} (rho ln rho)$ from $operatorname{Tr} (rho^n)$ for integer $n$ in a quantum system with density matrix $rho$. Instead of relying on direct analytic continuati
We perform a detailed analysis of holographic entanglement Renyi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Ei