Seminar: "A new large N expansion for tensor and matrix-tensor models" by Mr. Guillaume Valette

Speaker: Mr. Valette is currently in his last year as a Ph.D. student at Univ. Libre de Bruxelles, Belgium.

Abstract: In this talk, I will describe a new large N expansion for general tensor and matrix-tensor models based on arXiv:1709.07366. I will first recall the basics of uncolored tensor models introduced by Bonzom, Gurau and Rivasseau. Then, I will explain how one can obtain a more general large N expansion, working at all ranks and for all interactions, by enhancing the large N scaling of the coupling constants associated with these interactions. The new large N expansion is organized in terms of a quantity called the index, which has a nice combinatorial interpretation in terms of the matrix models embedded in the tensor model. In the second part, I will introduce matrix-tensor models, which are obtained by rewriting the tensor in terms of matrices. In these models, there is a new natural parameter D that allows one to define a large D expansion in addition to the large N one. I will discuss the interesting features of these two expansions. Finally, I will comment on the possible connection of matrix-tensor models with high-energy physics.