The $O(g^4)$ Lipatov Kernels

Leading plus next-to leading log results for the Regge limit of massless Yang-Mills theories are reproduced by reggeon diagrams in which the Regge slope $\alpha' \to 0$ and reggeon amplitudes satisfy Ward identity constraints at zero transverse momentum. Using reggeon unitarity together with multiple discontinuity theory a complete set of such diagrams can be constructed. The resulting two-two, one-three and two-four kernels which generalise the Lipatov equation at $O(g^4)$ are determined uniquely.