Geometrical Interpretation of the KPZ Exponents

Abstract

We provide evidence that the KPZ exponents in two-dimensional quantum gravity can be interpreted as scaling exponents of correlation functions which are functions of the invariant geodesic distance between the fields.

12 pages, LaTeX, 6 embedded figures with epsf, submitted to Phys.Lett. B., Minor style changes

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• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
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• Integrable 2D Lorentzian Gravity and Random Walks
• A global picture of quantum de Sitter space
• Quantum gravity as sum over spacetimes
• Quantum geometry of 2d gravity coupled to unitary matter
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Singular Structure in 4D Simplicial Gravity
• Relational observables in 2d quantum gravity
• The quantum space-time of c=-2 gravity
• New multicritical matrix models and multicritical 2d CDT
• CDT---an Entropic Theory of Quantum Gravity
• Black holes, information, and locality
• The Two-point Function of c=-2 Matter Coupled to 2D Quantum Gravity
• The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
• Ising and Potts Models on Quenched Random Gravity Graphs
• Liouville Quantum Gravity and KPZ
• Complex zeros of the 2d Ising model on dynamical random lattices
• The Hausdorff Dimension of Surfaces in Two-Dimensional Quantum Gravity Coupled to Ising Minimal Matter
• Random Surfaces and Lattice Gravity
• The Quantum Spacetime of c>0 2d Gravity
• 10 D Euclidean dynamical triangulations
• Perturbed generalized multicritical one-matrix models
• Scaling and Quantum Geometry in 2d Gravity
• 10 D Euclidean quantum gravity on the lattice
• Random walkers on a deformable medium