1,720,995 research outputs found
Holographic entanglement in group field theory
Full text linkThis work is meant as a review summary of a series of recent results concerning the derivation of a holographic entanglement entropy formula for generic open spin network states in the group field theory (GFT) approach to quantum gravity. The statistical group-field computation of the Rényi entropy for a bipartite network state for a simple interacting GFT is reviewed, within a recently proposed dictionary between group field theories and random tensor networks, and with an emphasis on the problem of a consistent characterisation of the entanglement entropy in the GFT second quantisation formalism
Typicality in spin-network states of quantum geometry
Full text linkIn this letter we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to SU(2) invariant spin network states. Our results do not depend on the physical interpretation of the spin-network, however they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the prove that, in that regime there are certain (local) properties of quantum geometry which are "universal". Such set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area-law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound
Generalized Gibbs Ensembles in Discrete Quantum Gravity
Full text linkMaximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum spacetime. We discuss the significant role played by information-theoretic characterizations of equilibrium. We present the Gibbs state description of the geometry of a tetrahedron and its quantization, thereby providing a statistical description of the characterizing quanta of space in quantum gravity. We use field coherent states for a generalized Gibbs state to write an effective statistical field theory that perturbatively generates 2-complexes, which are discrete spacetime histories in several quantum gravity approaches
Dissipation in Non-equilibrium Spacetime Thermodynamics
No full textIt has been recently realized [1, 2] that the thermodynamical derivation of the Einstein equation introduced by Jacobson [3] needs a generalization to a non-equilibrium thermodynamical setting. Here we show that the non-equilibrium character of spacetime thermodynamics - both in GR as well as in f(R) - gravity is generally related to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein's theory as an intrinsic property of gravitation
Fate of the Hoop Conjecture in Quantum Gravity
Full text linkWe consider a closed region of 3d quantum space modeled by spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity
Higher Curvature Gravity and the Holographic fluid dual to flat spacetime
Full text linkRecent works have demonstrated that one can construct a (d + 2) dimensional solution of the vacuum Einstein equations that is dual to a (d + 1) dimensional fluid satisfying the incompressible Navier-Stokes equations. In one important example, the fluid lives on a fixed timelike surface in the flat Rindler spacetime associated with an accelerated observer. In this paper, we show that the shear viscosity to entropy density ratio of the fluid takes the universal value 1/4 pi in a wide class of higher curvature generalizations to Einstein gravity. Unlike the fluid dual to asymptotically anti-de Sitter spacetimes, here the choice of gravitational dynamics only affects the second order transport coefficients. We explicitly calculate these in five-dimensional Einstein-Gauss-Bonnet gravity and discuss the implications of our results
Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian
Full text linkWe study the homogeneous extension of the Kullback-Leibler divergence associated to a covariant variational problem on the statistical bundle. We assume a finite sample space. We show how such a divergence can be interpreted as a Finsler metric on an extended statistical bundle, where the time and the time score are understood as extra random functions defining the model—-. We find a relation between the homogeneous generalisation of the Kullback-Leibler divergence and the Rényi relative entropy, the Rényi parameter being related to the time-reparametrization lapse of the Lagrangian model. We investigate such intriguing relation with an eye to applications in physics and quantum information theory
Group field theory and tensor networks: Towards a Ryu-Takayanagi formula in full quantum gravity
No full textWe 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 Rényi 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
Ryu-Takayanagi formula for symmetric random tensor networks
No full textWe consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi 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 into tensor network research
Statistical mechanics of reparametrization-invariant systems. It takes three to tango
No full textIt is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy, and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics. We focus on reparametrization-invariant systems without additional gauges. The key is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components - roughly: a clock and two systems among which a generalization of energy is equi-partitioned. This allows the application of statistical mechanics and thermodynamics as an additivity condition of such generalized energy
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