Abstract
We propose an identification of the conformal field theory underlying Lipatov's spin-chain model of high-energy scattering in perturbative QCD. It is a twisted N = 2 supersymmetric topological field theory, which arises as the limiting case of the SL(2,R)/U(1) non-linear $\sigma$ model that also plays a role in describing the Quantum Hall effect and black holes in string theory. The doubly-infinite set of non-trivial integrals of motion of the high-energy spin-chain model displayed by Faddeev and Korchemsky are identified as the Cartan subalgebra of a $W_{\infty} \otimes W_{\infty}$ bosonic sub-symmetry possessed by this topological theory. The renormalization group and an analysis of instanton perturbations yield some understanding why this particular topological spin-chain model emerges in the high-energy limit, and provide a new estimate of the asymptotic behaviour of multi-Reggeized-gluon exchange.
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