Turbulence and Random Geometry

We outline our proposal for a field theory description of steady state incompressible fluid turbulence at the inertial range of scales in a general number of space dimensions. The theory consists of a Kolmogorov linear scaling mean field theory dressed by a Nambu-Goldstone dilaton mode that induces a random measure on the inertial range. We derive a KPZ-type formula for the anomalous scalings of the velocity structure functions, the velocity gradients and the local energy dissipation, and relate the dimensionless intermittency parameter to the boundary conformal anomaly.