The Balitsky-Fadin-Kuraev-Lipatov (BFKL) formalism allowed giving a theoretical description of scattering amplitudes in the Regge limit of high energies and fixed momentum transfers in the framework of the theory of strong interactions, quantum chromodynamics (QCD).
Deep mathematical properties emerged in this way in the leading logarithmic approximation (LLA) for multi-colour QCD: conformal invariance, holomorphicfactorisation and integrability (Lipatov, 1986-1993). Moreover, in N=4 super-symmetric QCD these properties may hold in the next-to-leading approximation (NLLA) too. In such model, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for quasi-partonic operators are integrable in LLA (Lipatov, 1997) and possibly also in NLLA. We think that these remarkable features are related to the fact that N=4 super-symmetric QCD is dual to super-string theory according to the AdS/CFT correspondence.
We shall study in this project the relation between the integrability of evolution equations for high energy processes in gauge field theories and super-string theories paving the way to go beyond the traditional perturbation theory at least for N=4 super-symmetric QCD. The effective action constructed for gauge theories in the Reggelimit (Lipatov, 1995) will be investigated in QCD and in its super-symmetric generalisations to calculate next-to-next-to-leading corrections to the Regge trajectories and their couplings. The Reggeon field theory in QCD, derived in this way, will give a possibility to solve a long-standing problem of the unitarisation of the QCD pomeron. This is important for understanding the physics of quark-gluon matter created in the ultra-relativistic heavy ion collisions performed in BNL and CERN.
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