Renormalization and Hopf algebraic structure of the five-dimensional quartic tensor field theory

Avohou, Remi C.; Rivasseau, Vincent; Tanasă, Adrian

doi:10.1088/1751-8113/48/48/485204

Cited by 13 publications

(14 citation statements)

References 75 publications

(171 reference statements)

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“…Since our main task in this paper is lifting the matrix model theory to the tensor models, we rely upon the BZ-formalism in the presentation of [100] (see also [173] for an interesting related issue). Similar considerations can be also found in [83,84,174,175]. Though we do not go that far in this paper, the first really interesting tensor model to analyze within this context is the rainbow model of [25] (see also [77,78] for earlier works).…”

Section: Jhep06(2017)115supporting

confidence: 70%

Ward identities and combinatorics of rainbow tensor models

Itoyama¹,

Миронов²,

Морозов³

2017

J. High Energ. Phys.

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Abstract:We discuss the notion of renormalization group (RG) completion of nonGaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

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Section: Jhep06(2017)115supporting

confidence: 70%

Ward identities and combinatorics of rainbow tensor models

Itoyama¹,

Миронов²,

Морозов³

2017

J. High Energ. Phys.

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“…Finally the simplest tensor interaction V T is the color-symmetric sum of melonic [16,10] quartic interactions [17,18] where Trĉφφ means partial trace in H d = ⊗ d c=1 H c over all colors except c, and Tr c means trace over color c. The corresponding model is just renormalizable for d = 5 [19,20], which we now assume in this case.…”

Section: )mentioning

confidence: 99%

Why are tensor field theories asymptotically free?

Rivasseau

2015

EPL

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In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a 1/p 2 propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex, whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar φ 4 4 case, is simply due to the absence of any wave function renormalization at one loop.

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“…The current period centers around a more systematic investigation of their properties and phase structure, generalizing many standard field theoretic tools such as the parametric representation [53], renormalization group equations of the Polchinski [54] and Wetterich type [55,56], Ward identities combined with Schwinger-Dyson equations [57] and Connes-Kreimer algebras [58].…”

Section: Field Theoriesmentioning

confidence: 99%