Renormalization of a \(\mathrm{SU}(2)\) tensorial group field theory in three dimensions
type: Item
instance of: scholarly article
title: Renormalization of a \(\mathrm{SU}(2)\) tensorial group field theory in three dimensions
zbMATH Open document ID: 1300.83023
author: Sylvain Carrozza
author: Daniele Oriti
author: Vincent Rivasseau
published in: Communications in Mathematical Physics
publication date: 2014-07-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.6772
review text: The renormalizability of a \(\mathrm{SU}(2)\) tensorial group field theory in three dimensions is shown. This is part of the program to construct a (non-abelian) tensorial group field theory in four dimensions, which is hoped to describe quantum gravity. The analysis is based on concepts introduced in a previous work of the same authors [Commun. Math. Phys. 327, No. 2, 603--641 (2014; Zbl 1291.83102)], in particular the notion of face-connectedness of a graph. The proof of renormalizability uses multi-scale techniques.
reviewed by: Jochen Zahn
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 83C47
Mathematics Subject Classification ID: 81T15
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 83C80
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 6322653
zbMATH Keywords: tensorial group field theory
zbMATH Keywords: renormalization
zbMATH Keywords: multi-scale expansion
zbMATH Keywords: quantum gravity
zbMATH Keywords: face-connectedness of a graph
MaRDI profile type: Publication
OpenAlex ID: W3105255087
arXiv ID: 1303.6772
Wikidata QID: Q59239719
cites work: Q3447408
cites work: Q4648180
cites work: Modern Canonical Quantum General Relativity
cites work: Background independent quantum gravity: a status report
cites work: Q5423477
cites work: Crystallisation moves
cites work: The spin-foam approach to quantum gravity
cites work: A new spin foam model for 4D gravity
cites work: Flipped spinfoam vertex and loop gravity
cites work: LQG vertex with finite Immirzi parameter
cites work: Tensor models and simplicial quantum gravity in \(>2\)-D
cites work: Three-dimensional simplicial quantum gravity and generalized matrix models
cites work: Tensor model for gravity and orientability of manifold
cites work: Colored tensor models -- a review
cites work: Universality for random tensors
cites work: The \(1/N\) expansion of colored tensor models
cites work: The complete \(1/N\) expansion of colored tensor models in arbitrary dimension
cites work: Coupling of hard dimers to dynamical lattices via random tensors
cites work: Universality inp-spin glasses with correlated disorder
cites work: Critical behavior of colored tensor models in the large \(N\) limit
cites work: Phase transition in dually weighted colored tensor models
cites work: Classical group field theory
cites work: Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett–Crane model
cites work: A generalization of the Virasoro algebra to arbitrary dimensions
cites work: Toward classical geometrodynamics from the group field theory hydrodynamics
cites work: Deformed special relativity as an effective flat limit of quantum gravity
cites work: Effective Hamiltonian constraint from group field theory
cites work: Group field cosmology: a cosmological field theory of quantum geometry
cites work: Radiative corrections in the Boulatov-Ooguri tensor model: the 2-point function
cites work: Linearized group field theory and power-counting theorems
cites work: Bubble divergences from cellular cohomology
cites work: Bubble divergences from twisted cohomology
cites work: Bubble divergences: sorting out topology from cell structure
cites work: A renormalizable 4-dimensional tensor field theory
cites work: Addendum to: A renormalizable 4-dimensional tensor field theory
cites work: 3D tensor field theory: renormalization and one-loop \(\beta \)-functions
cites work: Two- and four-loop β-functions of rank-4 renormalizable tensor field theories
cites work: Bubbles and jackets: new scaling bounds in topological group field theories
cites work: Renormalization of tensorial group field theories: abelian \(\mathrm U(1)\) models in four dimensions
cites work: Some classes of renormalizable tensor models
cites work: Just renormalizable TGFT's on \(U(1)^d\) with gauge invariance
cites work: Constructive \(\phi^{4}\) field theory without tears
cites work: Scaling behavior of three-dimensional group field theory
cites work: Loop vertex expansion for Φ2k theory in zero dimension
cites work: Group field theory and simplicial quantum gravity
cites work: Encoding simplicial quantum geometry in group field theories
cites work: n-graphs
cites work: The classification of closed surfaces using colored graphs
cites work: A model of three-dimensional lattice gravity
DOI: 10.1007/S00220-014-1928-X
description: scientific article