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The Ryu-Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu-Takayangi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we propose that null rays emitted from the AdS boundary can be regarded as such a flow. In particular, we show that in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu-Takayanagi surfaces. In addition, based on the viewpoint of flow, we propose a wave optical formula to calculate the holographic entanglement entropy.
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We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R{e}nyi entropy of such states and recover the Ryu-Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.
I argue that a version of the quantum-corrected Ryu-Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the final statement expressed in the language of operator-algebra quantum error correction. In AdS/CFT this gives a purely boundary interpretation of the formula. I also extend a recent theorem, which established entanglement-wedge reconstruction in AdS/CFT, when interpreted as a subsystem code, to the more general, and I argue more physical, case of subalgebra codes. For completeness, I include a self-contained presentation of the theory of von Neumann algebras on finite-dimensional Hilbert spaces, as well as the algebraic definition of entropy. The results confirm a close relationship between bulk gauge transformations, edge-modes/soft-hair on black holes, and the Ryu-Takayanagi formula. They also suggest a new perspective on the homology constraint, which basically is to get rid of it in a way that preserves the validity of the formula, but which removes any tension with the linearity of quantum mechanics. Moreover they suggest a boundary interpretation of the bit threads recently introduced by Freedman and Headrick.
We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.
We study the phase transitions in the metal/superconductor system using topological invariants of the Ryu-Takayanagi ($RT$) surface and the volume enclosed by the $RT$ surface in the Lifshitz black hole background. It is shown that these topological invariant quantities identify not only the phase transition but also its order. According to these findings a discontinuity slope is observed at the critical points for these invariant quantities that correspond to the second order of phase transition. These topological invariants provide a clearer illustration of the superconductor phase transition than do the holographic entanglement entropy and the holographic complexity. Also, the backreaction parameter, $k$, is found to have an important role in distinguishing the critical points. The reducing values of the parameter $k$ means that the backreaction of the matter fields are negligible. A continuous slope is observed around the critical points which is characteristic of the probe limit. In addition, exploring the nonlinear electrodynamic, the effects of the nonlinear parameter, $beta$, is investigated. Finally the properties of conductivity are numerically explored in our model.
Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a generic base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the pp-waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions $n=5,6$ as well as for particular choices of the base manifold. The obtained solutions describe various classes of non-expanding gravitational waves propagating, e.g., in Nariai-like backgrounds $M_2timesSigma_{n-2}$. An appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N, and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.
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