On the Continuum Limit of the Conformal Matrix Models

TL;DR

This paper investigates the continuum limit of a new class of multi-matrix models with W-symmetry, showing they belong to the same universality class as standard models and detailing the transformation of W-algebras.

Contribution

It demonstrates the continuum limit of these models and the transformation of discrete W-algebras into their continuum counterparts, with explicit calculations for W^{(3)}-constraints.

Findings

Models share universality class with standard multi-matrix models

Transformation of W-algebra from discrete to continuum is established

Explicit calculations for W^{(3)}-constraints are provided

Abstract

The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the paper \cite{FKN91a} is proposed, the corresponding partition functions being compared. All calculations are demonstrated in full in the first non-trivial case of $W^{(3)}$-constraints.