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We study some analytic properties of the BFKL ladder at next-to-leadinglogarithmic accuracy (NLLA). We use a procedure by Chirilli and Kovchegov toconstruct the NLO eigenfunctions, and we show that the BFKL ladder can beevaluated order by order in the coupling in terms of certain generalisedsingle-valued multiple polylogarithms recently introduced by Schnetz. Wedevelop techniques to evaluate the BFKL ladder at any loop order, and wepresent explicit results up to five loops. Using the freedom in defining thematter content of the NLO BFKL eigenvalue, we obtain conditions for the BFKLladder in momentum space at NLLA to have maximal transcendental weight. Weobserve that, unlike in moment space, the result in momentum space in N = 4 SYMis not identical to the maximal weight part of QCD, and moreover that there isno gauge theory with this property. We classify the theories for which the BFKLladder at NLLA has maximal weight in terms of their field content, and we findthat these theories are highly constrained: there are precisely four classes oftheories with this property involving only fundamental and adjoint matter, allof which have a vanishing one-loop beta function and a matter content that fitsinto supersymmetric multiplets. Our findings indicate that theories which havemaximal weight are highly constrained and point to the possibility that thereis a connection between maximal transcendental weight and superconformalsymmetry.

The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy