Next-to-Leading Order in the Large N Expansion of the Multi-Orientable Random Tensor Model

Raasakka, Matti; Tanasă, Adrian

doi:10.1007/s00023-014-0336-2

Cited by 13 publications

(21 citation statements)

References 34 publications

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“…In this section we give a list of the results we have obtained throughout the paper. real SYK melonic Fig.1 (21) and (22) open an edge in (25), (26)…”

Section: Summary Of Resultsmentioning

confidence: 99%

Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders

Bonzom

Lionni

Tanasă

2017

Journal of Mathematical Physics

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The Sachdev-Ye-Kitaev (SYK) model is a model of q interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, those flavors are reminiscent of the colors used in random tensor theory. This gives us the opportunity to apply some modern, yet elementary, tools developed in the context of random tensors to one particular instance of such colored SYK models. We illustrate our method by identifying all diagrams which contribute to the leading and next-to-leading orders of the 2-point and 4-point functions in the large N expansion, and argue that our method can be further applied if necessary. In a second part we focus on the recently introduced Gurau-Witten tensor model and also extract the leading and next-to-leading orders of the 2-point and 4-point functions. This analysis turns out to be remarkably more involved than in the colored SYK model.

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“…In this section we give a list of the results we have obtained throughout the paper. real SYK melonic Fig.1 (21) and (22) open an edge in (25), (26)…”

Section: Summary Of Resultsmentioning

confidence: 99%

Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders

Bonzom

Lionni

Tanasă

2017

Journal of Mathematical Physics

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“…The latter are responsible for the last property of the model: the Lyapunov exponent, which measures the chaos in the system, reaches the maximal bound proposed in [7] and thus the system is maximally chaotic. All together these properties point towards a (near) AdS 2 /CFT 1 interpretation of the model (see [8][9][10][11] for references on near AdS 2 ). In gravitational theories the maximally chaotic objects are black holes: hence one can expect that the bulk dual of the SYK model contains black holes, and the fact that one can access the strong coupling regime offers an inestimable window on the quantum properties of black holes.…”

Section: Introductionmentioning

confidence: 82%

“…The next-to-leading order of the two-point function of the multi-orientable model has been studied in [28]. As the combinatorics is unchanged by the fact that we consider fermionic fields on one dimensional space we can easily infer the next-to-leading order in this case.…”

Section: The Next-to-leading Ordermentioning

confidence: 99%

“…This finding may have some implications for the construction of the bulk dual of SYK which has started in [59] (see also [4,9,56] and [74,75] for other proposals). Our method consists in analysing the transformation properties of the NLO 2-point function from the Schwinger-Dyson equation (the Feynman graphs contributing at this order have been studied in [58], see also [28]): this is sufficient to reach our conclusions except for the multi-orientable tensor model. In the latter case the conclusion depends on the explicit form of the NLO 2-point function and the full analysis is outside the scope of this paper.…”

Section: Introductionmentioning

confidence: 99%

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Conformality of 1/N corrections in Sachdev-Ye-Kitaev-like models

2019

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The Sachdev-Ye-Kitaev is a quantum mechanical model of N Majorana fermions which displays a number of appealing features -solvability in the strong coupling regime, nearconformal invariance and maximal chaos -which make it a suitable model for black holes in the context of the AdS/CFT holography. In this paper we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the N expansion preserves the conformal invariance of the 2-point function in the strong coupling regime, up to the contribution of the Goldstone bosons leading to the spontaneous breaking of the symmetry and which are already seen in the leading order 4-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models.

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“…The two terms appearing in the expression of the degree (17) are positive or 0. Hence they must both be 0 when ω = 0, leading to equations (19) and (20). Furthermore, it is easy to check that the class of degree-0 graphs is non-empty: for instance, the two graphs shown in Figure 4 have 0 degree.…”

Section: General Model and Large N Expansionmentioning

confidence: 99%

O(N) Random Tensor Models

2016

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We define in this paper a class of three indices tensor models, endowed with O(N ) ⊗3 invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N ) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.

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Next-to-Leading Order in the Large N Expansion of the Multi-Orientable Random Tensor Model

Cited by 13 publications

References 34 publications

Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders

Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders

Conformality of 1/N corrections in Sachdev-Ye-Kitaev-like models

O(N) Random Tensor Models

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