Non-analyticity in the large N renormalization group

TL;DR

This paper investigates how the action in large N matrix models changes with N, revealing a non-analytic behavior at the origin of the matrix space when the action is even, which impacts the understanding of large N renormalization group flows.

Contribution

It demonstrates that the change in the action with respect to N is non-analytic, providing new insights into the structure of large N matrix models and their renormalization group behavior.

Findings

Non-analytic change in the action at the origin of matrix space

Non-analyticity occurs when the action is even

Implications for large N renormalization group analysis

Abstract

The flow of the action induced by changing $N$ is computed in large $N$ matrix models. It is shown that the change in the action is non-analytic. This non-analyticity appears at the origin of the space of matrices if the action is even.