On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3

TL;DR

This paper introduces an algorithm to identify singularities in hermitean f-matrix models within the double scaling limit, confirming that only known universality classes from 2-matrix models are relevant for f >= 3.

Contribution

It provides a systematic method to analyze singularities in f-matrix models and proves the universality classes are consistent with those from 2-matrix models.

Findings

Only known universality classes from 2-matrix models exist for f >= 3

An algorithm for isolating singularities in f-matrix models is developed

The universality classes are confirmed through constructive proof

Abstract

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.