The 1/N expansion of colored tensor models in arbitrary dimension

Gurău, Razvan; Rivasseau, Vincent

doi:10.1209/0295-5075/95/50004

Cited by 188 publications

(270 citation statements)

References 37 publications

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“…This dominance was already observed in so-called "tensor models", and have been studied extensively in the literature [31][32][33][34][35][36][37][38][39][40][41]. Previously, except for [31], only bosonic tensor models had been considered with various form of interactions.…”

Section: Jhep08(2017)083mentioning

confidence: 87%

SYK-like tensor models on the lattice

Narayan

Yoon

2017

J. High Energ. Phys.

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Abstract:We study large N tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large N and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-D tensor models where we obtain analogous results as D = 3 case for the four point functions which we computed. For D > 5, we are able to compute the next-to-subleading 1 N corrections for a specific four point function.

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Section: Jhep08(2017)083mentioning

confidence: 87%

SYK-like tensor models on the lattice

Narayan

Yoon

2017

J. High Energ. Phys.

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“…Despite some initial pessimism [177], a recent spike of optimism occurred within the growing tensor model community, when it was discovered that a large class of such theories [18,[178][179][180][181][182] possessed a 1/ -expansion [183][184][185][186][187][188][189]; that is, their Feynman graphs could be partitioned into manageable subsets, using some parameter . In fact, it was shown that the leading order sector, in the largelimit, contained an infinite but manageable number of the Feynman graphs with the topology of the -sphere ( being the rank of the tensor).…”

Section: Tensor Models and Tensor Group Field Theoriesmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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“…Organizing the divergences occurring in the perturbation series of rank d colored tensor graphs, one introduces the following quantity called degree of the colored tensor graph G [43,44,45] …”

Section: Rank D > 2 Colored Stranded Graphsmentioning

confidence: 99%

“…Consider then a primitively divergent subgraph S ⊂ G, and a decomposition in Hepp sectors σ , t 1 ≤ t 2 ≤ · · · ≤ t L(S) of the lines of S and introduce the usual change of variables in x k as in (44). Because S is primitively divergent, for all subgraphs S) )) ≤ 0.…”

Section: Theorem 1 (Extended Domain Of Analyticity) Consider a Tensomentioning

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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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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The 1/N expansion of colored tensor models in arbitrary dimension

Abstract: In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S D contribute to the leading order in the large N limit.

Cited by 188 publications

References 37 publications

SYK-like tensor models on the lattice

SYK-like tensor models on the lattice

Spin Foam Models with Finite Groups

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

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