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We present an analytical method, rooted in the non-perturbativerenormalization group, that allows one to calculate the critical exponents andthe correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growthequation in all its different regimes, including the strong-coupling one. Weanalyze the symmetries of the KPZ problem and derive an approximation schemethat satisfies the linearly realized ones. We implement this scheme at theminimal order in the response field, and show that it yields a complete,qualitatively correct phase diagram in all dimensions, with reasonable valuesfor the critical exponents in physical dimensions. We also compute in onedimension the full (momentum and frequency dependent) correlation function, andthe associated universal scaling functions. We find an excellent quantitativeagreement with the exact results from Praehofer and Spohn (J. Stat. Phys. 115(2004)). We emphasize that all these results, which can be systematicallyimproved, are obtained with sole input the bare action and its symmetries,without further assumptions on the existence of scaling or on the form of thescaling function.

Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications