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Register a new userEntanglement entropy, horizons and holography
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We calculate the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, using holography. We employ appropriate parametrizations of AdS space in order to obtain a Rindler or static de Sitter boundary metric. The holographic entanglement entropy for the regions enclosed by the horizons can be identified with the standard thermal entropy of these spaces. For this to hold, we define the effective Newtons constant appropriately and account for the way the AdS space is covered by the parametrizations.
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The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the holographic representation are calculated by a method which does not require the solution of the equations of motion or a cut off. The two calculations disagree for rather generic geometries. The reasons for the disagreement are analyzed.
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 $AdS_{d+1}$ geometry and $AdS_{d+1}$-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.
We show that the gravitational phase space for the near-horizon region of a bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal symmetry algebra with central charges proportional to the area. This extends the construction of [Haco et. al., JHEP 12, 098 (2018)] to generic Killing horizons appearing in solutions of Einsteins equations, and motivates a holographic description in terms of a 2D conformal field theory. The Cardy entropy in such a field theory agrees with the Bekenstein-Hawking entropy of the horizon, suggesting a microscopic interpretation.
Many discussions in the literature of spacetimes with more than one Killing horizon note that some horizons have positive and some have negative surface gravities, but assign to all a positive temperature. However, the first law of thermodynamics then takes a non-standard form. We show that if one regards the Christodoulou and Ruffini formula for the total energy or enthalpy as defining the Gibbs surface, then the rules of Gibbsian thermodynamics imply that negative temperatures arise inevitably on inner horizons, as does the conventional form of the first law. We provide many new examples of this phenomenon, including black holes in STU supergravity. We also give a discussion of left and right temperatures and entropies, and show that both the left and right temperatures are non-negative. The left-hand sector contributes exactly half the total energy of the system, and the right-hand sector contributes the other half. Both the sectors satisfy conventional first laws and Smarr formulae. For spacetimes with a positive cosmological constant, the cosmological horizon is naturally assigned a negative Gibbsian temperature. We also explore entropy-product formulae and a novel entropy-inversion formula, and we use them to test whether the entropy is a super-additive function of the extensive variables. We find that super-additivity is typically satisfied, but we find a counterexample for dyonic Kaluza-Klein black holes.
We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in $phi^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.
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