Integrability properties of high energy dynamics in the multi-color QCD

It is shown that the interaction of reggeized gluons in the leading logarithmic approximation (LLA) of the multicolor QCD has a number of remarkable mathematical properties, including its conformal invariance, holomorphic factorization, and duality symmetry. The Reggeon Hamiltonian coincides with the Hamiltonian of the integrable Heisenberg model with the spins being the Möbius group generators. Using the Baxter–Sklyanin representation, we calculate intercepts of the colorless states constructed from three and four reggeized gluons and anomalous dimensions of the corresponding higher twist operators. To understand the origin of the integrability of high-energy dynamics in the multicolor QCD in the LLA, we investigate next-to-leading corrections to the BFKL and DGLAP equations in the $N=4$ supersymmetric gauge theory beyond the LLA.