Exact Solution of Discrete Two-Dimensional R^2 Gravity

Abstract

We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with an R^2 interaction. It permits us to study the intermediate regimes between the gravitating and flat metric. Flat space is modeled by a regular square lattice, while localised curvature is introduced through lattice defects. No ``flattening'' phase transition is found with respect to the R^2 coupling: the infrared behaviour of the system is that of pure gravity for any finite R^2 coupling. In the limit of infinite coupling, we are able to extract a scaling function interpolating between pure gravity and a dilute gas of curvature defects on a flat background. We introduce and explain some novel techniques concerning our method of large N character expansions and the calculation of Schur characters on big Young tableaux.

27 pages, 6 ps figures, uses harvmac.tex and epsf, minor changes

Cited by in corpus (40)

• Colored Tensor Models - a Review
• Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
• Phase Transition in Dually Weighted Colored Tensor Models
• On some integrals over the U(N) unitary group and their large N limit
• Integrable 2D Lorentzian Gravity and Random Walks
• Dilaton-gravity, deformations of the minimal string, and matrix models
• From Characters to Quantum (Super)Spin Chains via Fusion
• Fuzzy Scalar Field Theory as a Multitrace Matrix Model
• Octagons I: Combinatorics and Non-Planar Resummations
• Two-Matrix model with ABAB interaction
• Euclidian 4d quantum gravity with a non-trivial measure term
• Random normal matrices, Bergman kernel and projective embeddings
• A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
• Imposing causality on a matrix model
• Two-Dimensional Chiral Matrix Models and String Theories
• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Complex matrix model duality
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Phase Transition in Random Noncommutative Geometries
• The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
• On Products of Random Matrices
• Minimal Dynamical Triangulations of Random Surfaces
• Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces
• Freezing of Triangulations
• Hurwitz numbers from Feynman diagrams
• Three-Dimensional Simplicial Gravity and Degenerate Triangulations
• Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial
• Notes on conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string
• Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula
• Disc partition function of 2d $R^2$ gravity from DWG matrix model
• Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings
• The Two-Dimensional O(2) Model on a Random Planar Lattice at Strong Coupling
• A simple model of dimensional collapse
• 2D Quantum Gravity -Three States of Surfaces-
• A Flow in the Forest
• Probability around the Quantum Gravity. Part 1: Pure Planar Gravity
• Random manifolds and quantum gravity
• Counter-example to conjectured SU(N) character asymptotics
• Three-State Complex Valued Spins Coupled to Binary Branched Polymers in Two-Dimensional Quantum Gravity
• Branched polymers, complex spins and the freezing transition