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

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.

20 pages, REVTeX3.0 + epsf, 10 figures. 1 reference added. To appear in Nucl. Phys. B

Cited by in corpus (28)

• Nonperturbative Quantum Gravity
• Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models
• The spectral dimension of the branched polymers phase of two-dimensional quantum gravity
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Compact support probability distributions in random matrix theory
• Meanders: Exact Asymptotics
• Numerical Study of the Double Scaling Limit in Two-Dimensional Large N Reduced Model
• Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields
• Liouville quantum gravity with matter central charge in $(1,25)$: a probabilistic approach
• Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces
• Random Energy Model with complex replica number, complex temperatures and classification of the string's phases
• Exact Meander Asymptotics: a Numerical Check
• The tubular phase of self-avoiding anisotropic crystalline membranes
• A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?
• Random Surfaces and Lattice Gravity
• Liouville dynamical percolation
• Solution of Potts-3 and Potts-\infty Matrix Models with the Equations of Motion Method
• Renormalization Group for Matrix Models with Branching Interactions
• On touching random surfaces, two-dimensional quantum gravity and non-critical string theory
• The Two-Dimensional O(2) Model on a Random Planar Lattice at Strong Coupling
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• The F model on dynamical quadrangulations
• Topological Gravity with Non-Compact Matter
• Weak Liouville quantum gravity metrics with matter central charge $\mathbf{c}\in (-\infty ,25)$
• Three-State Complex Valued Spins Coupled to Binary Branched Polymers in Two-Dimensional Quantum Gravity
• New Analytical Results on Anisotropic Membranes
• Branched polymers, complex spins and the freezing transition
• Beyond the c=1 Barrier in Two-Dimensional Quantum Gravity