27 research outputs found

    Entanglement negativity, Holography and Black holes

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    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 dd-dimensional conformal field theories dual to bulk pure AdSd+1AdS_{d+1} geometry and AdSd+1AdS_{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.Comment: 32 pages, 3 figures, minor modification

    Holographic entanglement negativity for disjoint intervals in AdS3/CFT2AdS_3/CFT_2

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    We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in (1+1)(1+1) dimensional conformal field theories (CFT1+1CFT_{1+1}) through the AdS3/CFT2AdS_3/CFT_2 correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual CFT1+1CFT_{1+1}. The construction is utilized to compute the holographic entanglement negativity for such mixed states in CFT1+1CFT_{1+1}s dual to bulk pure AdS3AdS_3 geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.Comment: 17 pages, 4 figure

    Fast Scrambling of Mutual Information in Kerr-AdS4_4

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    We compute the disruption of mutual information between the hemispherical subsystems on the left and right CFTss of a Thermofield Double state described by a Kerr geometry in AdS4AdS_4 due to shockwaves along the equatorial plane. The shockwaves and the subsystems considered respect the axi-symmetry of the geometry. At late times the disruption of the mutual information is given by the lengthening of the HRT surface connecting the two subsystems, we compute the minimum value of the Lyapunov index-λL(min)\lambda_L^{(min)} at late times and find that it is bounded by κ=2πTH(1−μ L)\kappa=\frac{2\pi T_H}{(1-\mu\, \mathcal{L})} where μ\mu is the horizon velocity and L\mathcal{L} is the angular momentum per unit energy of the shockwave. At very late times we find the the scrambling time for such a system is governed by κ\kappa with κt∗=log⁡S\kappa t_*=\log \mathcal{S} for large black holes with large entropy S\mathcal{S}. We also find a term that increases the scrambling time by log⁡(1−μ L)−1\log(1-\mu\,\mathcal{L})^{-1} but which does not scale with the entropy of the Kerr geometry.Comment: 21-pages, 4-figure

    State Dependence of Krylov Complexity in 2d2d CFTs

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    We compute the Krylov Complexity of a light operator OL\mathcal{O}_L in an eigenstate of a 2d2d CFT at large central charge cc. The eigenstate corresponds to a primary operator OH\mathcal{O}_H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of OH\mathcal{O}_H is below or above the critical dimension hH=c/24h_H=c/24, marked by the 1st1st order Hawking-Page phase transition point in the dual AdS3AdS_3 geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d2d, and in the integrable 2d2d Ising CFT, where there is no such transition in the spectrum of states.Comment: 24 pages, 5 figures, minor corrections, references adde