# A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions

@article{PrezSnchez2021ARG, title={A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions}, author={Carlos I. P{\'e}rez-S{\'a}nchez}, journal={Letters in Mathematical Physics}, year={2021}, volume={112} }

We focus on functional renormalization for ensembles of several (say n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 1$$\end{document}) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form exp[-Tr(V1)×⋯×Tr(Vk)]\documentclass[12pt]{minimal…

## References

SHOWING 1-10 OF 36 REFERENCES

### Comment on “The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization”

- PhysicsJournal of High Energy Physics
- 2021

Recently, [JHEP12 131 (2020)] obtained (a similar, scaled version of) the (a, b)-phase diagram derived from the Kazakov-Zinn-Justin solution of the Hermitian two-matrix model with…

### Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models

- MathematicsJournal of Noncommutative Geometry
- 2022

A fuzzy geometry is a certain type of spectral triple whose Dirac operator crucially turns out to be a finite matrix. This notion was introduced in [J. Barrett, J. Math. Phys. 56, 082301 (2015)] and…

### On Multimatrix Models Motivated by Random Noncommutative Geometry I: The Functional Renormalization Group as a Flow in the Free Algebra

- MathematicsAnnales Henri Poincaré
- 2021

Random noncommutative geometry can be seen as a Euclidean path-integral quantization approach to the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of…

### Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

- Mathematics
- 2000

Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure…

### Formal multidimensional integrals, stuffed maps, and topological recursion

- Mathematics
- 2013

We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions. In terms of a 1d…

### On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model

- MathematicsAnnales Henri Poincaré
- 2022

We continue the study of fuzzy geometries inside Connes’ spectral formalism and their relation to multimatrix models. In this companion paper to Pérez-Sánchez (Ann Henri Poincaré 22:3095–3148, 2021,…

### Touching random surfaces and Liouville gravity.

- PhysicsPhysical review. D, Particles and fields
- 1995

Large [ital N] matrix models modified by terms of the form [ital g]([ital Tr][Phi][sup [ital n]])[sup 2] generate random surfaces which touch at isolated points. Matrix model results indicate that,…

### Noncommutative Geometry

- Mathematics
- 1997

Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In…

### Loop Models, Random Matrices and Planar Algebras

- Mathematics
- 2012

We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a…