# Sextic tensor field theories in rank 3 and 5

@article{Benedetti2019SexticTF,
title={Sextic tensor field theories in rank 3 and 5},
author={Dario Benedetti and Nicolas Delporte and Sabine Harribey and Ritam Sinha},
journal={Journal of High Energy Physics},
year={2019},
volume={2020},
pages={1-42}
}
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… Expand
14 Citations

#### Figures from this paper

Trifundamental quartic model
• Physics, Mathematics
• 2020
We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations,Expand
A large-$N$ tensor model with four supercharges
• Physics
• 2020
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 theExpand
Conformal symmetry and composite operators in the O(N )3 tensor field theory
• Physics
• Journal of High Energy Physics
• 2020
We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known asExpand
SO(3) -invariant phase of the O(N)3 tensor model
• Physics
• 2020
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 symmetryExpand
Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\varepsilon$ Expansion
• Physics
• 2020
The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-componentExpand
Flowing in discrete gravity models and Ward identities: a review
• Physics
• The European Physical Journal Plus
• 2021
Ward-Takahashi identities are nonperturbative expressions arising from symmetries in quantum and statistical field theories, as Noether currents conservation for classical theories. Since theirExpand
On the counting tensor model observables as U(N) and O(N) classical invariants
Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs,Expand
Sextic tensor model in rank $3$ at next-to-leading order
We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a U(N) symmetry andExpand
Remarks on a melonic field theory with cubic interaction
• Physics, Mathematics
• 2020
We revisit the Amit-Roginsky (AR) model in the light of recent studies on Sachdev-Ye-Kitaev (SYK) and tensor models, with which it shares some important features. It is a model of $N$ scalar fieldsExpand
Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion
• Physics
• 2021
The tensorial equations for non trivial fully interacting fixed points at lowest order in the e expansion in 4 − e and 3 − e dimensions are analysed for N-component fields and correspondingExpand

#### References

SHOWING 1-10 OF 103 REFERENCES
Line of fixed points in a bosonic tensor model
• Physics, Mathematics
• Journal of High Energy Physics
• 2019
A bstractWe 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 ofExpand
On large N limit of symmetric traceless tensor models
• Physics, Mathematics
• 2017
A bstractFor some theories where the degrees of freedom are tensors of rank 3 or higher, there exist solvable large N limits dominated by the melonic diagrams. Simple examples are provided by modelsExpand
A complex fermionic tensor model in d dimensions
• Physics
• 2017
A bstractIn this note, we study a melonic tensor model in d dimensions based on three-index Dirac fermions with a four-fermion interaction. Summing the melonic diagrams at strong coupling allows oneExpand
Multi-critical behaviour of 4-dimensional tensor models up to order 6
• Physics, Mathematics
• Nuclear Physics B
• 2019
Abstract Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a 1 / N expansion have been explored, most of them generatingExpand
Majorana fermion quantum mechanics for higher rank tensors
• Physics
• Physical Review D
• 2019
We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank five and higher. They are the non-random counterparts of the Sachdev-Ye-Kitaev (SYK)Expand
Conformal symmetry and composite operators in the O(N )3 tensor field theory
• Physics
• Journal of High Energy Physics
• 2020
We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known asExpand
Tensorial Gross-Neveu models
• Physics
• 2017
A bstractWe define and study various tensorial generalizations of the Gross-Neveu model in two dimensions, that is, models with four-fermion interactions and G3 symmetry, where we take either G =Expand
Prismatic large N models for bosonic tensors
• Physics
• Physical Review D
• 2018
We study the $O(N)^3$ symmetric quantum field theory of a bosonic tensor $\phi^{abc}$ with sextic interactions. Its large $N$ limit is dominated by a positive-definite operator, whose index structureExpand
Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions.
• Physics, Medicine
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
An improved method to describe the full theory space of the models where both short- and long-range propagator terms are present and no a priori choice among the two in the renormalization group flow is done is proposed. Expand
Notes on melonic O(N)q−1 tensor models
• Physics
• Journal of High Energy Physics
• 2018
A bstractIt has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N)q−1 agrees with the large N limit of the SYK model. In theseExpand