Two- and four-loop β-functions of rank-4 renormalizable tensor field theories

Geloun, Joseph Ben

doi:10.1088/0264-9381/29/23/235011

Cited by 78 publications

(110 citation statements)

References 62 publications

(174 reference statements)

Supporting

Mentioning

109

Contrasting

Order By: Relevance

“…We focus on models whose kinetic operator is the Laplace-Beltrami operator on SU(2) 4 , together with a 'mass term'. A motivation for this choice is that the presence of the Laplacian seems to be required by GFT renormalisation [65][66][67][68][69]. The equation (5.21) for the function ξ then becomes (setting the g ′′ I which are arbitrary equal to the identity)…”

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

137

256

View full text Add to dashboard Cite

We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

show abstract

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

137

256

View full text Add to dashboard Cite

show abstract

“…Such a factorization is necessary for undertaking the subsequent renormalization procedure of the models (22).…”

Section: Factorization Of the Amplitudesmentioning

confidence: 99%

“…Still in the case of N = 2 and for the just-renormalizable models (22), this term may lead to a mass sub-leading divergence.…”

Section: Lemma 3 (Factorization Of Amentioning

confidence: 99%

“…Another important remark is that any subtraction operator is defined by two actions: (1) the action of a Taylor operator on the amplitude integrand targeting specifically the variables which are associated with a primitively divergent subgraph S (using in particular scaling properties of Lemma 2) and (2) the subtraction of the pole induced by the diverging part for each term in the Taylor expansion. The procedure is completely standard at this stage for our models (22). Thus,…”

Section: Renormalizationmentioning

confidence: 99%

“…Nevertheless, we can study its properties as well. It is worth emphasizing that the following analysis does not specially focus on the models listed in (22). The amplitude (13) is completely general for a generic rank d ≥ 2 Abelian model with particular linear kinetic term.…”

Section: Polynomial Invariantsmentioning

confidence: 99%

See 2 more Smart Citations

Parametric representation of rank d tensorial group field theory: Abelian models with kinetic term ∑sps+μ

Geloun

Toriumi

2015

Journal of Mathematical Physics

View full text Add to dashboard Cite

We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank d Tensorial Group Field Theory. These models are called Abelian because their fields live on U (1) D . We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. New dimensional regularization and renormalization schemes are introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models φ 2n over U (1), and a matrix model over U (1) 2 . For all divergent amplitudes, we identify a domain of meromorphicity in a strip determined by the real part of the group dimension D. From this point, the ordinary subtraction program is applied and leads to convergent and analytic renormalized integrals. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank d Abelian models. We find that these polynomials do not satisfy the ordinary Tutte's rules (contraction/deletion). By scrutinizing the "face"-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.

show abstract

The tensor track, III

Rivasseau

2013

Fortschritte der Physik

100

View full text Add to dashboard Cite

We provide an informal up-to-date review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion, Osterwalder-Schrader positivity...) which, while important for the tensor track program, are not detailed in the usual quantum gravity literature. We list open questions in the conclusion and provide a rather extended bibliography.

show abstract

Two- and four-loop β-functions of rank-4 renormalizable tensor field theories

Cited by 78 publications

References 62 publications

Homogeneous cosmologies as group field theory condensates

Homogeneous cosmologies as group field theory condensates

Parametric representation of rank d tensorial group field theory: Abelian models with kinetic term ∑sps+μ

The tensor track, III

Contact Info

Product

Resources

About