Another derivation of the geometrical KPZ relations
David F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France) Bauer M. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
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.