Universality classes of the Kardar-Parisi-Zhang equation.

We reexamine mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling limit and show that there exist two branches of solutions. One branch (or universality class) exists only for dimensionalities d<dc=2 and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to dc=4 and gives values for the dynamical exponent z similar to those of numerical studies for d>or=2.