What unitary matrix models are not?

TL;DR

This paper investigates the critical behavior of unitary matrix models, revealing that only the first four critical points correspond to unitary theories and that their scaling solutions do not match those of branched polymer models.

Contribution

The study clarifies which critical points of unitary matrix models are physically meaningful and refutes a proposed connection to branched polymers.

Findings

Only the first four critical points have positive coefficients.

Critical points at k≥5 are non-unitary.

Scaling solutions differ from branched polymer models.

Abstract

We report results of two investigations of the double-scaling equations for the unitary matrix models. First, the fixed area partition functions have all positive coefficients only for the first four critical points. This implies that the critical points at $k\ge5$ describe non-unitary continuum theories. Secondly, we examine a conjectured connection to branched polymers, but find that the scaling solutions of the unitary models do not agree with those of a particular model describing branched polymers.