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We show the result for the BFKL Pomeron intercept at N = 4 SYM in the form of the inverse coupling expansion j0 = 2 − 2λ−1/2 − λ−1 + 1/4λ−3/2 + 2(1 + 3ζ3)λ−2 + O(λ−5/2), which has been calculated in [1] with the use of the AdS/CFT correspondence.

We consider scattering amplitudes in QCD at high energies \(\sqrt s \) and fixed momentum transfers \(q = \sqrt { - t} \) with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit Nc → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.

We present results for the universal anomalous dimension γuni(j) of Wilson twist-2 operators in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory.

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.