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

The c1 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.Comment: 20 pages, REVTeX3.0 + epsf, 10 figures. 1 reference added. To appear in Nucl. Phys.

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure