The 1 / N Expansion of the Symmetric Traceless and the Antisymmetric Tensor Models in Rank Three

Benedetti, Dario; Carrozza, Sylvain; Gurău, Razvan; Kolanowski, Maciej

doi:10.1007/s00220-019-03551-z

Cited by 37 publications

(75 citation statements)

References 43 publications

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“…That is the leading order graphs are melonic after substituting all the pillows and double-trace vertices by their minimal realizations in terms of the tetrahedral vertex. In terms of the original interactions in G, one gets melon tadpole [45] graphs, that is graphs obtained by iterated insertions of melons or tadpoles into melons or tadpoles, see Fig. 4.…”

Section: Feynman Graphsmentioning

confidence: 99%

Line of fixed points in a bosonic tensor model

Benedetti

Gurău

Harribey

2019

J. High Energ. Phys.

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149

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We consider the O(N ) 3 tensor model of Klebanov and Tarnopolsky [1] in d < 4 with a free covariance modified to fit the infrared conformal scaling. We study the renormalization group flow of the model using a Wilsonian approach valid in any d (notably we do not require d = 4 − with small ). At large N , the tetrahedral coupling has a finite flow, hence it becomes a free parameter. The remaining flow can be parameterized by two couplings which do not mix. We show that, at leading order in 1/N but non perturbatively in the couplings, the beta functions stop at quadratic order in the pillow and double-trace couplings. We find four fixed points which depend parametrically on the tetrahedral coupling. For purely imaginary values of the latter we identify a real and infrared attractive fixed point. We remark that an imaginary tetrahedral coupling is in fact natural from the onset as the tetrahedral invariant does not have any positivity property, and moreover in the large-N limit the beta functions depend on the square of the tetrahedral coupling, thus they remain real, as long as the other couplings stay real.

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Section: Feynman Graphsmentioning

confidence: 99%

Line of fixed points in a bosonic tensor model

Benedetti

Gurău

Harribey

2019

J. High Energ. Phys.

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149

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“…While the tensor models [1] exhibit the same properties at the large N limit, they do not have disorder therefore giving us hope that they can be understood at finite N via standard techniques of quantum field theories. These techniques have already brought many interesting results [17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric tensor model at large N and small ε

Popov

2020

Phys. Rev. D

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We study the O(N ) 3 supersymmetric quantum field theory of a scalar superfield Φ abc with a tetrahedral interaction. In the large N limit the theory is dominated by the melonic diagrams. We solve the corresponding Dyson-Schwinger equations in continuous dimensions below 3. For sufficiently large N we find an IR stable fixed point and computed the 3 − expansion up to the second order of perturbation theory, which is in agreement with the solution of DS equations. We also describe the 1 + expansion of the model and discuss the possiblity of adding the Chern-Simons action to gauge the supersymmetric model.

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“…Tensor models with O(N ) symmetry are more complicated to analyze, and they have a well-defined large-N limit only if one restricts to one of the irreducible components of the product of representations, as shown in Ref. [30,31] following a conjecture made in Ref. [32].…”

Section: Spontaneous Symmetry Breaking At the Classical Levelmentioning

confidence: 99%

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
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We study classical and quantum (at large-N ) field equations of bosonic tensor models with quartic interactions and O(N ) 3 symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an SO(3) invariant solution, with the tensor field expressed in terms of the Wigner 3jm symbol. We argue that such solution has a special role in the large-N limit, as in particular its scaling in N can provide an on-shell justification for the melonic large-N limit of the two-particle irreducible effective action in a broken phase.

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The 1 / N Expansion of the Symmetric Traceless and the Antisymmetric Tensor Models in Rank Three

Cited by 37 publications

References 43 publications

Line of fixed points in a bosonic tensor model

Line of fixed points in a bosonic tensor model

Supersymmetric tensor model at large N and small ε

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite

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The 1 / N Expansion of the Symmetric Traceless and the Antisymmetric Tensor Models in Rank Three

Cited by 37 publications

References 43 publications

Line of fixed points in a bosonic tensor model

Line of fixed points in a bosonic tensor model

Supersymmetric tensor model at large N and small ε

SO(3) -invariant phase of the O(N)3Benedetti1, Costa2 2020Phys. Rev. DSelf Cite140110View full textAdd to dashboardCite

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SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite