Abstract In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the analysis of the Dyson–Schwinger equations (DSE) in the large N limit. These results are essential to implement the double scaling limit mechanism of the DSEs, which is done in the third section. The main result of this chapter is the doubly-scaled 2-point function for a model with generic melonic interactions. However, several assumptions on the large N scaling of cumulants are made along the way. They are proved using various combinatorial methods.Abstract In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the analysis of the Dyson–Schwinger equations (DSE) in the large N limit. These results are essential to implement the double scaling limit mechanism of the DSEs, which is done in the third section. The main result of this chapter is the doubly-scaled 2-point function for a model with generic melonic interactions. However, several assumptions on the large N scaling of cumulants are made along the way. They are proved using various combinatorial methods.

Apr 16, 20210 citations

A REVIEW OF THE LARGE N LIMIT OF TENSOR MODELS

Razvan Gurău

WORLD SCIENTIFIC eBooksAug 14, 201315 citations

The full Schwinger-Dyson tower for random tensor models

Carlos I. Pérez-Sánchez

We treat random rank- $D$ tensor models as $D$ -dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the obtention of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the obtention of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.

arXiv:1808.07075Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)Aug 22, 20180 citations

New 1/N expansions in random tensor models

Valentin Bonzom

arXiv:1211.1657Journal of High Energy PhysicsJun 1, 201377 citations

Phase diagram and criticality of the random anisotropy model in the large- N limit

D. Mouhanna, Gilles Tarjus

We revisit the thermodynamic behavior of the random-anisotropy O( $N$ ) model by investigating its large- $N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large- $N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible ``glassy'' phases. Finally we discuss the implications of our findings for the finite- $N$ and finite-temperature systems.We revisit the thermodynamic behavior of the random-anisotropy O($N$) model by investigating its large-$N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-$N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible ``glassy'' phases. Finally we discuss the implications of our findings for the finite-$N$ and finite-temperature systems.

arXiv:1607.08515Physical review. B./Physical review. BDec 29, 20167 citations

We treat random rank-

D

tensor models as

D

-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the obtention of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.

We revisit the thermodynamic behavior of the random-anisotropy O(

N

) model by investigating its large-

N

limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-

N

limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible ``glassy'' phases. Finally we discuss the implications of our findings for the finite-

N

and finite-temperature systems.