Abstract
An exact relation between the Green's function and the dressed third-order vertex \ensuremath{\Gamma} was found for the Kardar-Parisi-Zhang (KPZ) model of surface roughening in (1+d) dimensions. This relation, of the Ward-identity type, follows from a hidden symmetry of the problem, which generalizes in some sense the Galilean invariance of the KPZ equation. This relation allows one to conclude that in the region of strong coupling, \ensuremath{\Gamma}-${\mathrm{\ensuremath{\Gamma}}}_{0}$\ensuremath{\sim}0.1${\mathrm{\ensuremath{\Gamma}}}_{0}$, where ${\mathrm{\ensuremath{\Gamma}}}_{0}$ is the bare value of the vertex \ensuremath{\Gamma}. The identity is generalized for higher-order vertices, enabling us to predict some relations between observable correlation functions.
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