Critical behavior of colored tensor models in the large N limit

Bonzom, Valentin; Gurău, Razvan; Riello, Aldo; Rivasseau, Vincent

doi:10.1016/j.nuclphysb.2011.07.022

Cited by 289 publications

(527 citation statements)

References 60 publications

(114 reference statements)

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“…The simplest is to make the couplings Ji 1 ...iq be nearly static quantum variables [28]. A better way of eliminating disorder is to turn SYK into a tensor model [29] (see also, [30][31][32]), analogous to the ones previously studied [33][34][35][36][37]. To leading order in 1/N all these approaches agree.…”

Section: Fermion Four-point Functionmentioning

confidence: 99%

The bulk dual of SYK: cubic couplings

Gross

Rosenhaus

2017

J. High Energ. Phys.

155

200

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The SYK model, a quantum mechanical model of N 1 Majorana fermions χ i , with a q-body, random interaction, is a novel realization of holography. It is known that the AdS 2 dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the 1/N expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large N dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large q.

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Section: Fermion Four-point Functionmentioning

confidence: 99%

The bulk dual of SYK: cubic couplings

Gross

Rosenhaus

2017

J. High Energ. Phys.

155

200

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“…Furthermore, GFT renormalization is also one of the two main strategies to define and study the renormalization of spin foam models, the other being through a generalised lattice gauge theory approach [22]. Most work in this direction has concerned a particular class of GFTs, called Tensorial Group Field Theories (TGFT's) [23][24][25][26][27][28][29][30][31][32][33], which incorporate recent advances in the statistical analysis of colored tensor models [34][35][36][37]. In particular, in TGFT framework, fields are endowed with tensorial transformation properties under the action of the group itself.…”

mentioning

confidence: 99%

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

Geloun

Martini

Oriti

2015

EPL

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-We study a model of Tensorial Group Field Theory (TGFT) on R 3 from the point of view of the Functional Renormalisation Group. This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on R) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.Introduction. -Group Field Theories [1-5] (GFTs) are a particular class of quantum field theories with fields defined over a group manifold and characterised by combinatorially non-local interaction terms. This combinatorial non-locality makes the Feynman diagrams of the theory stranded diagrams dual to cellular complexes (simplicial complexes in the simplest constructions) [1,3]. GFT's historically were born from an attempt to generalise matrix models [6] of 2d gravity to higher dimensions in the form of tensor models [7][8][9]. These models were soon enriched with group theoretic data in such a way that the Feynman amplitudes of specific GFT models coincide with state sum models of topological field theory [9,10]. A connection between GFTs and Loop Quantum Gravity (LQG) [11,12] was immediately pointed out [13] at the level of quantum states, and later enforced at the level of the quantum dynamics. In fact, it was later shown [14] that GFTs provide a formal (complete) definition of spin foams models, a covariant formalism for LQG. For GFTs (and spin foam models) endowed with a discrete geometric interpretation (which requires appropriate group theoretic data and suitable choices of dynamics) there is also a direct link with simplicial quantum gravity path integrals, first manifested in the semiclassical analysis of GFT Feynman (spin foam) amplitudes, where one recovers the Regge action [15], and then shown to be generically manifest in the flux repre-

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“…A graph for which ω(G) = 0 is called a "melon" or "melonic" graph [50]. This quantity is at the core of the extension of the notion of genus expansion (t'Hooft large N expansion in matrix models) now for colored tensor models.…”

Section: Rank D > 2 Colored Stranded Graphsmentioning

confidence: 99%

“…This quantity is at the core of the extension of the notion of genus expansion (t'Hooft large N expansion in matrix models) now for colored tensor models. It is at the basis of the success of finding a way to analytically resum the perturbation series in colored tensor models at leading order and even beyond [50]- [63].…”

Section: Rank D > 2 Colored Stranded Graphsmentioning

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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Critical behavior of colored tensor models in the large N limit

Cited by 289 publications

References 60 publications

The bulk dual of SYK: cubic couplings

The bulk dual of SYK: cubic couplings

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

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

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