The microscopic dynamics of quantum space as a group field theory

Abstract

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on some recent results obtained in this approach, concerning both the mathematical definition of GFT models as bona fide field theories, and possible avenues towards extracting interesting physics from them.

Homogeneous cosmologies as group field theory condensates

“…However, to understand better the motivation of the GFT approach, let us explain more closely the relation of group field theories [22][23][24][25][26][27][28] to loop quantum gravity (LQG) [14][15][16] and specifically its spin foam corner [17,18], which has in fact provided the impetus for the development of group field theories. More details on this are given in a separate publication [29] but we illuminate the most important points here.…”

Group field theory in dimension4−ϵ

“…Group Field Theory (GFT) [1][2][3][4] is a general formalism aiming at completing the definition of the dynamics of Loop Quantum Gravity (LQG) [5][6][7][8][9], either from a covariant perspective as was historically proposed and since then has been the main line of investigation [10,11], or directly from the canonical picture as was more recently suggested [12,13]. An alternative but related approach to the same question relies on lattice gauge theory methods [14][15][16][17].…”

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

“…-Group Field Theories [1][2][3][4][5] (GFTs) are a particular class of quantum field theories with fields defined over a group manifold and characterised by combinatorially non-local interaction terms. This combinatorial non-locality makes the Feynman diagrams of the theory stranded diagrams dual to cellular complexes (simplicial complexes in the simplest constructions) [1,3]. GFT's historically were born from an attempt to generalise matrix models [6] of 2d gravity to higher dimensions in the form of tensor models [7][8][9].…”

“…The term ∆S k is also chosen to be compatible with the choice of initial conditions for the FRG differential equation, encoding the scaling of effective action to the bare one in 1 We adopt the standard QFT terminology for field modes, even though no spacetime interpretation is associated to the domain of the fields, and thus no standard physical interpretation should be associated to their modes. The same remark applies to our use of the terms 'UV' and 'IR' throughout the article.…”