Maximal Transcendentality and Integrability

The Hamiltonian describing possible interactions of the Reggeized gluons in the leading logarithmic approximation (LLA) of the multicolor QCD has the properties of conformal invariance, holomorphic separability and duality. It coincides with the Hamiltonian of the integrable Heisenberg model with the spins being the Moebius group generators. With the use of the Baxter-Sklyanin representation we calculate intercepts of the colorless states constructed from three and four Reggeized gluons and anomalous dimensions of the corresponding high twist operators. The integrability properties of the BFKL equation at a finite temperature are reviewed. Maximal transcendentality is used to construct anomalous dimensions of twist-2 operators up to 4 loops. It is shown that the asymptotic Bethe Ansatz in the 4-loop approximation is not in an agreement with predictions of the BFKL equation in N = 4 SUSY. (author)