One-loop QCD spin chain and its spectrum

We study the renormalization of gauge invariant operators in large N-c QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with selfdual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation. (c) 2005 Elsevier B.V. All rights reserved.