  The Kardar-Parisi-Zhang universality class of stochastic surface growth is
studied by exact field-theoretic methods. From previous numerical results, a
few qualitative assumptions are inferred. In particular, height correlations
should satisfy an operator product expansion and, unlike the correlations in a
turbulent fluid, exhibit no multiscaling. These properties impose a
quantization condition on the roughness exponent $\chi$ and the dynamic
exponent $z$. Hence the exact values $\chi = 2/5, z = 8/5$ for two-dimensional
and $\chi = 2/7, z = 12/7$ for three-dimensional surfaces are derived.
