Multi-color QCD at High Energies and Exactly Solvable Lattice Theories

Abstract

We examine the generalized leading-logarithmic approximation (LLA) equations for compound states of n-reggeized gluons. It is shown that in multi-color QCD, when $N_c\to \infty$, these equations have a sufficient number of conservation laws to be exactly solvable. Holomorphic factorization of the wave functions is used to reduce the corresponding quantum mechanical problem to the solution of the one-dimensional Heisenberg model with the spins being the generators of the M$\ddot{o}$bius group of conformal transformations.

11 pages, latex, no figures, to appear in Proceedings of the workshop 'Theory of Hadrons and Light-Front QCD', Poland, August 1994, Lipatov's invited talk at this meeting