On the Perturbation Expansion of the KPZ- Equation

Thanks to a fluctuation dissipation theorem and the mapping to exactly solvable models, much is known for space-dimension d = 1 [1, 2, 3]. In contrast, the case of d ≥ 2 can only be attacked by approximative methods or field-theoretic perturbative expansions. Using the latter, the fixed point structure of the renormalization group flow for d = 2 + ε has been obtained [1, 4, 5]. Two domains can be distinguished: For small effective coupling