scholarly journals Group Field Theory and Its Cosmology in a Matter Reference Frame

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 103 ◽  
Author(s):  
Steffen Gielen
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Coordinate System ◽  
Reference Frame ◽  
Degrees Of Freedom ◽  
Reference Frames ◽  
Scalar Fields ◽  
General Idea ◽  
Theory Approach ◽  
Group Field Theory

While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where coordinates are not a priori available and need to be reconstructed from physical degrees of freedom. We review the general idea of coupling free scalar fields to gravity and using these scalars as a “matter reference frame”. The resulting coordinate system is harmonic, i.e., it satisfies the harmonic (de Donder) gauge. We then show how to introduce such matter reference frames in the group field theory approach to quantum gravity, where spacetime is emergent from a “condensate” of fundamental quantum degrees of freedom of geometry, and how to use matter coordinates to extract physics. We review recent results in homogeneous and inhomogeneous cosmology, and give a new application to the case of spherical symmetry. We find tentative evidence that spherically-symmetric group field theory condensates defined in this setting can reproduce the near-horizon geometry of a Schwarzschild black hole.

scholarly journals Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luca Marchetti ◽  
Daniele Oriti ◽  
Andreas G. A. Pithis ◽  
Johannes Thürigen
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Phase Transitions ◽  
Quantum Gravity ◽  
Compact Group ◽  
Large Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Theory Approach ◽  
Non Local

Abstract In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including ℝ-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.

scholarly journals Spin Foam Models with Finite Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-28 ◽  
Author(s):  
Benjamin Bahr ◽  
Bianca Dittrich ◽  
James P. Ryan
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Finite Groups ◽  
Loop Quantum Gravity ◽  
Theory Approach ◽  
Test Bed ◽  
Spin Foam Models ◽  
Spin Foam ◽  
Group Field Theory ◽  
The Many

Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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 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.

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