Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions

Carrozza, Sylvain; Oriti, Daniele; Rivasseau, Vincent

doi:10.1007/s00220-014-1928-x

Cited by 135 publications

(219 citation statements)

References 97 publications

(197 reference statements)

Supporting

Mentioning

211

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%

See 1 more Smart Citation

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

Self Cite

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%

“…Again, we can assume that the kinetic term of the GFT model consists of a Laplacian and a mass term. For the coordinates on H 3 that are the analogue of the coordinates on S 3 chosen above, the Laplacian is 67) so that (5.21) reduces to…”

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

Self Cite

137

256

View full text Add to dashboard Cite

show abstract

“…Another class of models has been the focus of studies [28] aiming at extending standard renormalization tools to GFTs and at proving renormalizability of specific models, relying heavily on the recent results of the simpler tensor models [30], and thus referred to as tensorial GFTs or TGFTs. In particular, TGFTs use a new notion of locality: tensor invariance (related to invariance under U (N ) d transformations, where N is a cut-off on the Lie algebra dual to G).…”

Section: B the Gft Frameworkmentioning

confidence: 99%

Disappearance and emergence of space and time in quantum gravity

Oriti

2014

Studies in History and Philosophy of Science Part B: Studies in

Self Cite

111

View full text Add to dashboard Cite

We discuss the hints for the disappearance of continuum space and time at microscopic scale. These include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory of gravity. We discuss how these ideas are realized in specific quantum gravity approaches. Turning then the problem around, we consider the emergence of continuum space and time from the collective behaviour of discrete, pre-geometric atoms of quantum space, and for understanding spacetime as a kind of "condensate", and we present the case for this emergence process being the result of a phase transition, dubbed "geometrogenesis". We discuss some conceptual issues of this scenario and of the idea of emergent spacetime in general. As a concrete example, we outline the GFT framework for quantum gravity, and illustrate a tentative procedure for the emergence of spacetime in this framework. Last, we re-examine the conceptual issues raised by the emergent spacetime scenario in light of this concrete example.

show abstract

“…The result of a hard contraction can be inferred from this point. We will focus on (24) and on (25), since the rest of the relations falls quite from the definitions.…”

Section: Definition 6 (Sets Of Faces) For All S ⊂ Gmentioning

confidence: 99%

“…-To achieve (25), one notes that, after the complete hard contraction of all lines in S, F int (S) is mapped to the empty set. Indeed, a closed face f in S either becomes shorter and shorter after (hard or soft) contraction whenever there still exists a line l ∈ f .…”

Section: Definition 6 (Sets Of Faces) For All S ⊂ Gmentioning

confidence: 99%

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

Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions

Cited by 135 publications

References 97 publications

Homogeneous cosmologies as group field theory condensates

Homogeneous cosmologies as group field theory condensates

Disappearance and emergence of space and time in quantum gravity

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

Contact Info

Product

Resources

About