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Particles and Fields
Eur. Phys. J. C 8, 91-102
DOI 10.1007/s100529901047

High-energy QCD as a topological field theory

J. Ellis1 - N.E. Mavromatos2

1 Theory Division, CERN, CH-1211 Geneva 23, Switzerland
2 P.P.A.R.C. Advanced Fellow, University of Oxford, Department of Physics (Theoretical Physics), 1 Keble Road OX1 3NP, UK

Received: 31 August 1998 / Published online: 11 March 1999

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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