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Register a new userSecond-order Lovelock Gravity from Entanglement in Conformal Field Theories
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Holographic entanglement entropy and the first law of thermodynamics are believed to decode the gravity theory in the bulk. In particular, assuming the Ryu-Takayanagi (RT)cite{ryu-takayanagi} formula holds for ball-shaped regions on the boundary around CFT vacuum states impliescite{Nonlinear-Faulkner} a bulk gravity theory equivalent to Einstein gravity through second-order perturbations. In this paper, we show that the same assumptions can also give rise to second-order Lovelock gravity. Specifically, we generalize the procedure in cite{Nonlinear-Faulkner} to show that the arguments there also hold for Lovelock gravity by proving through second-order perturbation theory, the entropy calculated using the Wald formulacite{Wald_noether} in Lovelock also obeys an area law (at least up to second order). Since the equations for second-order perturbations of Lovelock gravity are different in general from the second-order perturbation of the Einstein-Hilbert action, our work shows that the holographic area law cannot determine a unique bulk theory even for second-order perturbations assuming only RT on ball-shaped regions. It is anticipated that RT on all subregions is expected to encode the full non-linear Einstein equations on asymptotically AdS spacetimes.
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In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einsteins equations perturbatively up to second order, with a stress energy tensor arising from matter fields associated with the sourced primary operators. We make no assumptions about AdS/CFT duality, so our work serves as both a consistency check for the AdS/CFT correspondence and a direct demonstration that spacetime and gravitational physics can emerge from the description of entanglement in conformal field theories.
We derive dynamics of the entanglement wedge cross section directly from the two-dimensional holographic CFTs with a local operator quench. This derivation is based on the reflected entropy, a correlation measure for mixed states. We further compare these results with the mutual information and ones for RCFTs. Our results directly suggest the classical correlation also plays an important role in the subregion/subregion duality even for dynamical setup. Besides a local operator quench, we study the reflected entropy in a heavy state and provide improved bulk interpretation. We checked the above results also hold for the odd entanglement entropy, which is another measure for mixed states related to the entanglement wedge cross section.
It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$ space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small $epsilon$. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in $d=2$.
We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples.
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points are close to the real axis, the system typically exhibits walking behavior with Miransky (or Berezinsky-Kosterlitz-Thouless) scaling. We present a novel realization of these phenomena at strong coupling by means of the gauge/gravity duality, and give evidence for the conjectured existence of complex conformal field theories at the fixed points.
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