  We propose an effective conformal field theory (CFT) description of steady
state incompressible fluid turbulence at the inertial range of scales in any
number of spatial dimensions. We derive a KPZ-type equation for the anomalous
scaling of the longitudinal velocity structure functions and relate the
intermittency parameter to the boundary Euler (A-type) conformal anomaly
coefficient. The proposed theory consists of a mean field CFT that exhibits
Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a
Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the
energy flux of the separate scale and time symmetries of the inviscid
Navier-Stokes equations to a K41 scaling with a dynamical exponent
$z=\frac{2}{3}$. The dilaton acts as a random measure that dresses the K41
theory and introduces intermittency. We discuss the two, three and large number
of space dimensions cases and how entanglement entropy can be used to
characterize the intermittency strength.
