High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed nonperturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent ? decays not faster than ?~1/d for large d. This implies the absence of a finite upper critical dimension.