BFKL pomeron at non-zero temperature and integrability of the reggeon dynamics in multi-colour QCD

Abstract

We consider the QCD scattering amplitudes at high energies s and fixed momentum transfers −t in the leading logarithmic approximation at a non-zero temperature T in the t-channel. It is shown that the BFKL Hamiltonian has the property of holomorphic separability. The pomeron wave function for arbitrary T is calculated using an integral of motion. In multi-colour QCD, the holomorphic Hamiltonian for n-reggeized gluons at temperature T is shown to coincide with the local Hamiltonian of an integrable Heisenberg model and can be obtained from the T=0 Hamiltonian by an unitary transformation. We discuss the wave functions and the spectrum of intercepts for the colourless reggeon states.