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Register a new userGroup Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
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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.
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We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the Renyi entropy for a bipartite network state using the partition function of a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu- Takayanagi formula. For a simple interacting group field theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.
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.
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.
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.
We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the FLRW background for this kind of models. Restricting to homogeneous scalar field configurations in the action, we derive degeneracy conditions to obtain an effective field theory with three degrees of freedom. However, performing the Hamiltonian analysis for a generic scalar field we show that there are in general four or more degrees of freedom. The discrepancy is resolved because, for a homogeneous scalar field profile, $partial_ivarphiapprox 0$, the Dirac matrix becomes singular, resulting in further constraints, which reduces the number of degrees of freedom to three. Similarly, in linear perturbation theory the additional scalar degree of freedom can only be seen by considering a non-homogeneous background profile of the scalar field. Therefore, restricting to homogeneous scalar fields these kinds of models provide viable explicitly Lorentz violating effective field theories of mimetic gravity.
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