Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-16
Nucl.Phys. B645 (2002) 237-297
Physics
High Energy Physics
High Energy Physics - Theory
57 pages, Latex style, 10 figures; discussion in sections 5 and 6 extended, references and comment added
Scientific paper
10.1016/S0550-3213(02)00842-8
We present a complete description of the spectrum of compound states of reggeized gluons in QCD in multi-colour limit. The analysis is based on the identification of these states as ground states of noncompact Heisenberg SL(2,C) spin magnet. A unique feature of the magnet, leading to many unusual properties of its spectrum, is that the quantum space is infinite-dimensional and conventional methods, like the Algebraic Bethe Ansatz, are not applicable. Our solution relies on the method of the Baxter Q-operator. Solving the Baxter equations, we obtained the explicit expressions for the eigenvalues of the Q-operator. They allowed us to establish the quantization conditions for the integrals of motion and, finally, reconstruct the spectrum of the model. We found that intercept of the states built from even (odd) number of reggeized gluons, N, is bigger (smaller) than one and it decreases (increases) with N approaching the same unit value for infinitely large N.
Derkachov Sergey E.
Korchemsky Gregory P.
Kotanski Jan
Manashov Alexander N.
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