We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in (1 + 1)-dimensional conformal field theories in the AdS 3 /CF T 2 framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the CF T 1+1 vacuum dual to bulk the pure AdS 3 geometry and the finite temperature mixed state dual to a Euclidean BTZ black hole respectively. The holographic entanglement negativity characterizes the distillable entanglement and reduces to a specific sum of holographic mutual informations. We briefly allude to a possible higher dimensional generalization of our conjecture in a generic AdS d+1 /CF T d scenario.

We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an SL(2, R) × U(1) global symmetry. We present comparisons on symmetries, correlation functions, the effective action and the entropy formula. We also use modular covariance to reinterpret results in the complex SYK model. arXiv:1808.08062v2 [hep-th] 8 Dec 2018

We investigate the application of our recent holographic entanglement negativity conjecture for higher dimensional conformal field theories to specific examples which serve as crucial consistency checks. In this context we compute the holographic entanglement negativity for bipartite pure and finite temperature mixed state configurations in d-dimensional conformal field theories dual to bulk pure Ad S d+1 geometry and Ad S d+1 -Schwarzschild black holes respectively. It is observed that the holographic entanglement negativity characterizes the distillable entanglement for the finite temperature mixed states through the elimination of the thermal contributions. Significantly our examples correctly reproduce universal features of the entanglement negativity for corresponding two dimensional conformal field theories, in higher dimensions.

The holographic quantum entanglement entropy for an infinite strip region of the boundary for the field theory dual to charged black holes in AdS 3+1 is investigated. In this framework we elucidate the low and high temperature behavior of the entanglement entropy pertaining to various limits of the black hole charge. In the low temperature regime we establish a first law of entanglement thermodynamics for the boundary field theory. *