O(N) Random Tensor Models
- Sylvain Carrozza, A. Tanasa
- Mathematics
- 21 December 2015
We define in this paper a class of three-index tensor models, endowed with $${O(N)^{\otimes 3}}$$O(N)⊗3 invariance (N being the size of the tensor). This allows to generate, via the usual QFT…
A Translation-Invariant Renormalizable Non-Commutative Scalar Model
- R. Gurau, J. Magnen, V. Rivasseau, A. Tanasa
- Mathematics
- 6 February 2008
In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders…
Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
The Sachdev-Ye-Kitaev (SYK) model is a model of q interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different flavors. In terms of…
The Multi-Orientable Random Tensor Model, a Review
- A. Tanasa
- Mathematics
- 7 December 2015
After its introduction (initially within a group eld theory framework) in A. Tanasa, J. Phys. A 45 (2012) 165401, the multi-orientable (MO) tensor model grew over the last years into a solid…
Hopf algebras and Tutte polynomials
- T. Krajewski, I. Moffatt, A. Tanasa
- MathematicsAdvances in Applied Mathematics
- 4 August 2015
Combinatorial Physics
- A. Tanasa
- Mathematics
After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main…
Generalization of the Bollobás-Riordan polynomial for tensor graphs
- A. Tanasa
- Mathematics
- 8 December 2010
Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a…
Quantum corrections in the group field theory formulation of the Engle-Pereira-Rovelli-Livine and Freidel-Krasnov models
- T. Krajewski, J. Magnen, V. Rivasseau, A. Tanasa, P. Vitale
- Physics
- 30 December 2010
We investigate the group field theory formulation of the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK spin-foam models. These models aim at a dynamical, i.e., nontopological formulation of…
SOLUTIONS FOR THE CONSTANT QUANTUM YANG-BAXTER EQUATION FROM LIE (SUPER)ALGEBRAS
- A. Tanasa, Á. Ballesteros, F. J. H. L. Orsay, Univ. Burgos
- Mathematics
- 25 April 2007
Author(s): Tanasa, A.; Ballesteros, A.; Herranz, F. J. | Abstract: We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension.…
Asymptotic Expansion of the Multi-Orientable Random Tensor Model
This paper analyzes the general term of the asymptotic expansion in N, the size of the tensor, of a particular random Tensor model, the multi-orientable tensor model of three-dimensional random tensor models.
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