Notes on Tensor Models and Tensor Field Theories

Gurău, Razvan

doi:10.48550/arxiv.1907.03531

Cited by 10 publications

(21 citation statements)

References 102 publications

(186 reference statements)

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“…The full four-point function at leading order in 1/N is obtained by summing ladders of arbitrary lenghts with the (reduced) four-point kernel acting as rung (see [34,56]). More precisely, defining the forward four-point function as…”

Section: Rankmentioning

confidence: 99%

“…In order to better understand the conformal field theory at such IR fixed points, 14 we wish to compute the spectrum of operators that appear in the operator-product expansion (OPE) of φ abc (x) φabc (0). Schematically, these are expected to be the bilinear operators φ abc (∂ 2 ) n φabc , and their spectrum can be obtained using the conformal Bethe-Salpeter (BS) equation [29,42], or equivalently, the spectral decomposition of the four-point function [35,56,64].…”

Section: The ζ = Dmentioning

confidence: 99%

“…The four-point function of our CFT can be written in a standard represent-theoretic form as [56,64,65]:…”

Section: The ζ = Dmentioning

confidence: 99%

“…where h m,J are the poles of (1 − k ζ (h, J)) −1 , and the squares of the OPE coefficients are the residues at the poles [35,56,64]. We will limit ourselves to just studying the location of the poles, i.e.…”

Section: The ζ = Dmentioning

confidence: 99%

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Sextic tensor field theories in rank 3 and 5

Benedetti

Delporte

Harribey

et al. 2020

J. High Energ. Phys.

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We study bosonic tensor field theories with sextic interactions in d < 3 dimensions. We consider two models, with rank-3 and rank-5 tensors, and U(N) 3 and O(N) 5 symmetry, respectively. For both of them we consider two variations: one with standard short-range free propagator, and one with critical long-range propagator, such that the sextic interactions are marginal in any d < 3. We derive the set of beta functions at large N , compute them explicitly at four loops, and identify the respective fixed points. We find that only the rank-3 models admit melonic interacting fixed points, with real couplings and critical exponents: for the short-range model, we have a Wilson-Fisher fixed point with couplings of order √ , in d = 3 − ; for the long-range model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g 1 (associated to the so-called wheel interaction). By standard conformal field theory methods, we then study the spectrum of bilinear operators associated to such interacting fixed points, and we find a real spectrum for small or small g 1 .

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Section: Rankmentioning

confidence: 99%

Section: The ζ = Dmentioning

confidence: 99%

“…The four-point function of our CFT can be written in a standard represent-theoretic form as [56,64,65]:…”

Section: The ζ = Dmentioning

confidence: 99%

Section: The ζ = Dmentioning

confidence: 99%

See 2 more Smart Citations

Sextic tensor field theories in rank 3 and 5

Benedetti

Delporte

Harribey

et al. 2020

J. High Energ. Phys.

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“…In recent years, there has been an increasing interest in a new large-N behaviour: the melonic limit of tensor models [4][5][6][7]. This particular limit arises when we study models with N r fields transforming in the fundamental representation of O(N ) r .…”

Section: Introductionmentioning

confidence: 99%

A large-$N$ tensor model with four supercharges

Lettera¹,

Vichi²

2020

Preprint

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We study a supersymmetric tensor model with four supercharges and O(N ) 3 global symmetry. The model is based on a chiral scalar superfield with three indices and quartic tetrahedral interaction in the superpotential, which is relevant below three dimensions. In the large-N limit the model is dominated by melonic diagrams. We solve the Dyson-Schwinger equations in superspace for generic d and extract the dimension of the chiral field and the dimensions of bilinear operators transforming in various representations of O(N ) 3 . We find that all operator dimensions are real and above the unitarity bound for 1 < d < 3. Our results also agree with perturbative results in 3 − ε expansion. Finally, we extract the large spin behaviour of bilinear operators and discuss the connection with lightcone bootstrap.

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Hints of unitarity at large N in the O(N )3 tensor field theory

Benedetti

Gurău

Harribey

et al. 2020

J. High Energ. Phys.

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We compute the OPE coefficients of the bosonic tensor model of [1] for three point functions with two fields and a bilinear with zero and non-zero spin. We find that all the OPE coefficients are real in the case of an imaginary tetrahedral coupling constant, while one of them is not real in the case of a real coupling. We also discuss the operator spectrum of the free theory based on the character decomposition of the partition function.

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Notes on Tensor Models and Tensor Field Theories

Cited by 10 publications

References 102 publications

Sextic tensor field theories in rank 3 and 5

Sextic tensor field theories in rank 3 and 5

A large-$N$ tensor model with four supercharges

Hints of unitarity at large N in the O(N )3 tensor field theory

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