Another derivation of the geometrical KPZ relations

Abstract

We give a physicist's derivation of the geometrical (in the spirit of Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2d quantum gravity, and shows that these relations are in the realm of conformal field theory.

References in corpus (5)

• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• Conformally Invariant Fractals and Potential Theory
• The Spectral Dimension of 2D Quantum Gravity

Cited by in corpus (6)

• Duality and KPZ in Liouville Quantum Gravity
• Liouville Brownian motion
• Liouville heat kernel: regularity and bounds
• Spectral dimension of Liouville quantum gravity
• Spanning Forests on Random Planar Lattices
• Dimension result and KPZ formula for two-dimensional multiplicative cascade processes