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 ${\mathit{z}}_{\mathit{c}}$ at the KPZ roughening transition. Our argument does not rely on perturbation theory and predicts that the value ${\mathit{z}}_{\mathit{c}}$=2 should be superuniversal, whenever thermal fluctuations are relevant at the corresponding equilibrium critical point in the directed polymer model.