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Authors
Elena Caceres
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We use the Iyer-Wald formalism to derive an extended first law of entanglement that includes variations in the cosmological constant, Newtons constant and --in the case of higher-derivative theories-- all the additional couplings of the theory. In Einstein gravity, where the number of degrees of freedom $N^2$ of the dual field theory is a function of $Lambda$ and $G$, our approach allows us to vary $N$ keeping the field theory scale fixed or to vary the field theory scale keeping $N$ fixed. We also derive an extended first law of entanglement for Gauss-Bonnet and Lovelock gravity and show that in these cases all the extra variations reorganize nicely in terms of the central charges of the theory. Finally, we comment on the implications for renormalization group flows and c-theorems in higher dimensions.
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We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in $(1+1)$-dimensional conformal field theories in the $AdS_3/CFT_2$ framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the $CFT_{1+1}$ 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 $AdS_{d+1}/CFT_{d}$ scenario.
We propose a covariant holographic conjecture for the entanglement negativity of mixed states in bipartite systems described by $d$-dimensional conformal field theories dual to bulk non static $AdS_{d+1}$ configurations. Application of our conjecture to $(1+1)$-dimensional conformal field theories dual to bulk rotating BTZ black holes exactly reproduces the corresponding entanglement negativity in the large central charge limit and characterizes the distillable entanglement. We further demonstrate that our conjecture applied to the case of bulk extremal rotating BTZ black holes also characterizes the entanglement negativity for the chiral half of the corresponding zero temperature $(1+1)$-dimensional holographic conformal field theories.
We study the behavior of holographic entanglement entropy (HEE) for imbalanced holographic superconductors. We employ a numerical approach to consider the robust case of fully back-reacted gravity system. The hairy black hole solution is found by using our numerical scheme. Then it is used to compute the HEE for the superconducting case. The cases we study show that in presence of a mismatch between two chemical potentials, below the critical temperature, superconducting phase has a lower HEE in comparison to the AdS-Reissner-Nordstrom black hole phase. Interestingly, the effects of chemical imbalance are different in the contexts of black hole and superconducting phases. For black hole, HEE increases with increasing imbalance parameter while it behaves oppositely for the superconducting phase. The implications of these results are discussed.
We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the $T bar{T}$ deformation. Under the boost and $T bar{T}$ deformation, the $c$-function of the entanglement entropy exactly shows the features expected by the Zamoldchikovs $c$-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincare cutoff AdS space can reproduce the exact same result of the $T bar{T}$ deformed theory on a two-dimensional sphere.
We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.
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