From the Quantum Spectral Curve, the authors derive the Asymptotic Baxter-Bethe Ansatz, which determines the asymptotic BFKL spectrum of Regge trajectories in N=4 SYM, reproduces known weak-coupling results, and supports a conjectured strong-coupling intercept spectrum.
Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
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abstract
We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.
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Regge Trajectories of N=4 SYM Part I: General Asymptotic Baxter-Bethe Ansatz
From the Quantum Spectral Curve, the authors derive the Asymptotic Baxter-Bethe Ansatz, which determines the asymptotic BFKL spectrum of Regge trajectories in N=4 SYM, reproduces known weak-coupling results, and supports a conjectured strong-coupling intercept spectrum.