Tensor Models: extending the matrix models structures and methods

2016/03/07 by Stéphane Dartois, Dartois, Stephane
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1603.02167

openalex publication_date 2016/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor models. Despite the generic title of this review, we, in particular, invoke the Topological Recursion. We explain its appearance in matrix models. Then we state that a family of tensor models provides a natural example which satisfies a version of the most general form of the topological recursion, named the blobbed topological recursion. We discuss the difficulties of extending the technical solutions existing for matrix models to tensor models. Some proofs are not published yet but will be given in a coming paper, the rest of the results are well known in the literature.

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