scholarly journals The Multi-Orientable Random Tensor Model, a Review

2016 ◽  
Author(s):  
Adrian Tanasa ◽  
Keyword(s):  
Tensor Model ◽  
Random Tensor

scholarly journals Asymptotic Expansion of the Multi-Orientable Random Tensor Model

10.37236/4629 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Eric Fusy ◽  
Adrian Tanasa
Keyword(s):  
Asymptotic Expansion ◽  
Matrix Models ◽  
Three Dimensional ◽  
Natural Generalization ◽  
General Term ◽  
Tensor Model ◽  
Half Integer ◽  
Tensor Models ◽  
Random Tensor

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expanion in $N$, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

scholarly journals A random matrix model with non-pairwise contracted indices

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Luca Lionni ◽  
Naoki Sasakura
Keyword(s):  
Matrix Model ◽  
Random Matrix ◽  
Spherical Model ◽  
Tensor Model ◽  
Probabilistic Interpretation ◽  
Random Matrix Model ◽  
The Matrix ◽  
Replicated Systems ◽  
Random Tensor

Abstract We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the $p$-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.

The Sachdev–Ye–Kitaev (SYK) holographic model

2021 ◽  
pp. 260-290
Author(s):  
Adrian Tanasa
Keyword(s):  
Gaussian Distribution ◽  
Mechanical Model ◽  
Quantum Mechanical ◽  
Tensor Model ◽  
Holographic Model ◽  
Leading Order ◽  
Tensor Models ◽  
Feynman Graphs ◽  
Non Gaussian ◽  
Random Tensor

In this chapter, we first review the Sachdev–Ye–Kitaev (SYK) model, which is a quantum mechanical model of N fermions. The model is a quenched model, which means that the coupling constant is a random tensor with Gaussian distribution. The SYK model is dominated in the large N limit by melonic graphs, in the same way the tensor models presented in the previous three chapters are dominated by melonic graphs. We then present a purely graph theoretical proof of the melonic dominance of the SYK model. It is this property which led E. Witten to relate the SYK model to the coloured tensor model. In the rest of the chapter we deal with the so-called coloured SYK model, which is a particular case of the generalisation of the SYK model introduced by D. Gross and V. Rosenhaus. We first analyse in detail the leading order and next-to-leading order vacuum, two- and four-point Feynman graphs of this model. We then exhibit a thorough asymptotic combinatorial analysis of the Feynman graphs at an arbitrary order in the large N expansion. We end the chapter by an analysis of the effect of non-Gaussian distribution for the coupling of the model.

scholarly journals W-representation of Rainbow tensor model

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Bei Kang ◽  
Lu-Yao Wang ◽  
Ke Wu ◽  
Jie Yang ◽  
Wei-Zhong Zhao
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Crucial Role ◽  
Elementary Function ◽  
Tensor Model ◽  
Witt Algebra ◽  
Virasoro Constraints ◽  
Compact Expression ◽  
Non Gaussian ◽  
Dual Expression

Abstract We analyze the rainbow tensor model and present the Virasoro constraints, where the constraint operators obey the Witt algebra and null 3-algebra. We generalize the method of W-representation in matrix model to the rainbow tensor model, where the operators preserving and increasing the grading play a crucial role. It is shown that the rainbow tensor model can be realized by acting on elementary function with exponent of the operator increasing the grading. We derive the compact expression of correlators and apply it to several models, i.e., the red tensor model, Aristotelian tensor model and r = 4 rainbow tensor model. Furthermore, we discuss the case of the non-Gaussian red tensor model and present a dual expression for partition function through differentiation.

scholarly journals Mother canonical tensor model

2017 ◽  
Vol 34 (14) ◽  
pp. 145009 ◽  
Author(s):  
Gaurav Narain ◽  
Naoki Sasakura
Keyword(s):  
Tensor Model

scholarly journals Geometrically constrained two-tensor model for crossing tracts in DWI

2006 ◽  
Vol 24 (9) ◽  
pp. 1263-1270 ◽  
Author(s):  
Sharon Peled ◽  
Ola Friman ◽  
Ferenc Jolesz ◽  
Carl-Fredrik Westin
Keyword(s):  
Tensor Model ◽  
Geometrically Constrained
Sign in / Sign up

Export Citation Format

Share Document