scholarly journals Quantum gravity states, entanglement graphs and second-quantized tensor networks

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eugenia Colafranceschi ◽  
Daniele Oriti
Keyword(s):  
Quantum Information ◽  
Quantum Gravity ◽  
Classical Limit ◽  
Microscopic Structure ◽  
Dual Representation ◽  
Diffeomorphism Invariance ◽  
Tensor Networks ◽  
Discrete Counterpart ◽  
Physical Level ◽  
Group Field Theory

Abstract In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation in terms of graphs and simplicial complexes. We devote special attention to the implementation and consequences of the label independence of the graphs/networks, corresponding to the indistinguishability of the space quanta and representing a discrete counterpart of the diffeomorphism invariance of a consistent quantum gravity formalism. We also outline a relational setting to recover distinguishability of graph/network vertices at an effective and physical level, in a partial semi-classical limit of the theory.

scholarly journals Cosmological constraints on a classical limit of quantum gravity

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
Damien A. Easson ◽  
Frederic P. Schuller ◽  
Mark Trodden ◽  
Mattias N. R. Wohlfarth
Keyword(s):  
Quantum Gravity ◽  
Classical Limit ◽  
Cosmological Constraints

Quantum gravity, group field theory (GFT), and combinatorics

2021 ◽  
pp. 121-165
Author(s):  
Adrian Tanasa
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Specific Model ◽  
Algebraic Combinatorics ◽  
Saddle Point Method ◽  
Feynman Integrals ◽  
Causal Dynamical Triangulations ◽  
Group Field Theory ◽  
Definition Of

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

scholarly journals Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 107 ◽  
Author(s):  
Marco de Cesare
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Effective Field ◽  
Time Varying ◽  
Reconstruction Procedure ◽  
Cosmological Background ◽  
Bouncing Universe ◽  
Physical Information ◽  
Group Field Theory ◽  
Mimetic Gravity

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power-law expansions of f in different regimes, corresponding e.g., to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational “constants” in the cosmological equations.

scholarly journals Holographic Entanglement in Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 211 ◽  
Author(s):  
Goffredo Chirco
Keyword(s):  
Field Theory ◽  
Entanglement Entropy ◽  
Bipartite Network ◽  
Spin Network ◽  
Network State ◽  
Tensor Networks ◽  
Holographic Entanglement Entropy ◽  
Group Field Theory ◽  
Network States ◽  
Random Tensor

This 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.

scholarly journals Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 41 ◽  
Author(s):  
Bekir Baytaş ◽  
Martin Bojowald ◽  
Sean Crowe
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Canonical Realization ◽  
Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

Fermions, q-deformed diffeomorphism and the evolution of spin networks

2015 ◽  
Vol 24 (10) ◽  
pp. 1550074 ◽  
Author(s):  
L. Mullick ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Closed Loop ◽  
Direction Vector ◽  
Spin Networks ◽  
Spin Network ◽  
Diffeomorphism Invariance ◽  
Diffeomorphism Symmetry

We have considered here the emergence of diffeomorphism symmetry in quantum gravity in the framework of the quantization of a fermion. It is pointed out that a closed loop having the holonomy associated with the SU(2) gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting spin degrees of freedom which appear as SU(2) gauge bundle. During the formation of a loop, a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves q-deformed gauge group SUq(2). This gives rise to q-deformed diffeomorphism and helps to realize diffeomorphism invariance in quantum gravity through a sequence of q-deformed diffeomorphism in the limit q = 1. We can consider adiabatic iteration such that the quasispin associated with the quantum group SUq(2) gradually evolves as the time dependent deformation parameter q changes and in the limit q = 1, we achieve the standard spin. This essentially depicts the evolution of spin network as the loop is being formed and links fermionic degrees of freedom with loop quantum gravity.

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