Analytic continuation of harmonic sums with imaginary indices near integer values

V. N. Velizhanin

Published 2022-10-25Version 1

We present a simple algebraic method for the analytic continuation of harmonic sums with real or imaginary indices near negative and positive integers. We provide a MATHEMATICA code for exact expansion of harmonic sums in a small parameter near these integers. As an application, we consider the analytic continuation of the anomalous dimension of twist-1 operators in ABJM model, which contains the nested harmonic sums with imaginary indices. We found that in the BFKL-like limit the result has the same single-logarithmic behavior as in N=4 SYM and QCD, however, we did not find a general expression for the ``BFKL Pomeron'' eigenvalue in this model. For the slope function, we found full agreement with the expansion of the known general result and give predictions for the first three perturbative terms in the expansion of the next-to-slope function. The proposed method of analytic continuation can also be used for other generalisations of nested harmonic sums.