Tensorial Methods and Renormalization in Group Field Theories

Carrozza, Sylvain

doi:10.1007/978-3-319-05867-2

Cited by 66 publications

(112 citation statements)

References 93 publications

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“…It is simply a subtraction operator acting on the amplitude which will prove to lead to a convergent integral. There is of course a way to make this operator compatible with Hepp sectors and has been defined in the context of TGFT models [8].…”

Section: Renormalizationmentioning

confidence: 99%

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

Geloun

Toriumi

2015

Journal of Mathematical Physics

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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.

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Section: Renormalizationmentioning

confidence: 99%

“…It is only recent that the notion of large N expansion was extended to tensor models [43]- [45] (for however the class of colored models [46]- [48]). From this point, important progresses have been unlocked [49]- [63] and a renormalization program for tensor models uncovered (for a review, see [8,27]). …”

Section: Introductionmentioning

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

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“…The renormalizable models studied so far divide into two main categories, those without [49,50] and with [14,51,52] Boulatov-type group field theory projectors, which we should nickname respectively as TFTs and TGFT's. TGFTs are TFT's with the particular additional "gauge invariance" implemented by the Boulatov projector 3 .…”

Section: Field Theoriesmentioning

confidence: 99%

“…There are several reviews addressing particular subtopics and even books published [14] or in preparation. Hence this note is not intended as a review but rather as an introductory guide to the recent results, structured around four brief sections…”

Section: Introductionmentioning

confidence: 99%

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Tensor Field Theory

Rivasseau¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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The tensor track, III

Rivasseau

2013

Fortschritte der Physik

100

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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.

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Tensorial Methods and Renormalization in Group Field Theories

Cited by 66 publications

References 93 publications

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

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

Tensor Field Theory

The tensor track, III

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