Exact dynamical exponent at the Kardar-Parisi-Zhang roughening transition

We use a mapping of the Kardar-Parisi-Zhang (KPZ) equation for interfacial growth to the equilibrium model of a directed polymer in a random medium to obtain the exact value of the dynamical exponent zc at the KPZ roughening transition. Our argument does not rely on perturbation theory and predicts that the value zc=2 should be superuniversal, whenever thermal fluctuations are relevant at the corresponding equilibrium critical point in the directed polymer model.