Hidden symmetry, exact relations, and a small parameter in surface growth models with diffusion

An exact relation between the Greenʹs function and the dressed three-point vertex function Γ was found for the Langevin equations describing surface growth with diffusion in 1 + d dimensions. This relation follows from a hidden symmetry of the problem with a gauge function depending on time only and turns out to be exactly the same as that found by Lebedev and Lʹvov for the Kardar-Parisi-Zhang (KPZ) equation of surface roughening. By a similar analysis as was done for the KPZ equation we conclude that in the region of strong coupling Γ − Γ 0.1Γ0, where Γ0 is the bare value of the vertex Γ.