Critical discussion of the two-loop calculations for the Kardar-Parisi-Zhang equation

In this paper, we perform a careful analysis of the renormalization procedure used in existing calculations to derive critical exponents for the Kardar-Parisi-Zhang equation at two-loop order. This analysis explains the discrepancies between the results of the different groups. The correct critical exponents in d=2+ɛ dimensions at the crossover between the weak- and strong-coupling regime are χ=O(ɛ³) and z=2+O(ɛ³). No strong-coupling fixed point exists at two-loop order.