A scenario for the c>1 barrier in non-critical bosonic strings

TL;DR

This paper explores the phase structure of non-critical bosonic string models with central charge c>1, proposing that their critical behavior resembles branched polymers and analyzing the transition at c=1.

Contribution

It introduces a renormalization group analysis of matrix models with touching interactions, revealing the disappearance of fixed points at c=1 and characterizing the c>1 phase as branched polymer-like.

Findings

Fixed points merge and vanish at c=1.

c>1 models exhibit branched polymer behavior.

Pseudo-scaling explains numerical results near c=1.

Abstract

The c<1 and c>1 matrix models are analyzed within large N renormalization group, taking into account touching (or branching) interactions. The c<1 modified matrix model with string exponent gamma>0 is naturally associated with an unstable fixed point, separating the Liouville phase (gamma<0) from the branched polymer phase (gamma=1/2). It is argued that at c=1 this multicritical fixed point and the Liouville fixed point coalesce, and that both fixed points disappear for c>1. In this picture, the critical behavior of c>1 matrix models is generically that of branched polymers, but only within a scaling region which is exponentially small when c -> 1. It also explains the behavior of multiple Ising spins coupled to gravity. Large crossover effects occur for c-1 small enough, with a c ~ 1 pseudo-scaling which explains numerical results.