Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensio ns with Gaussian spatially long-range correlated noise - characterized by i ts second moment R(x - x') proportional to \x - x'\(2 rho-d) - by means of dynamic field theory and the renormalization group. Using a stochastic Cole -Hopf transformation we derive exact exponents and scaling functions for th e roughening transition and the smooth phase above the lower critical dimen sion d(c) = 2((1+rho)). Below the lower critical dimension, there is a line rho(*)(d) marking the stability boundary between the short-range and long- range noise fixed points. For rho greater than or equal to rho(*)(d), the g eneral structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above rho(*)(d), one has to rely on some perturbational techniques. We discuss the location of t his stability boundary rho(*)(d) in light of the exact results derived in t his paper, and from results known in the literature. In particular, we conj ecture that there might be two qualitatively different strong-coupling phas es above and below the lower critical dimension, respectively.