ABJM quantum spectral curve and Mellin transform

Understand

The present techniques for the perturbative solution of quantum spectral curve problems in N=4 SYM and ABJM models are limited to the situation when the states quantum numbers are given explicitly as some integer numbers.

• These techniques are sufficient to recover full analytical structure of the conserved charges provided that we know a finite basis of functions in terms of which they could be written explicitly.
• It is known that in the case of N=4 SYM both the contributions of asymptotic Bethe ansatz and wrapping or finite size corrections are expressed in terms of the harmonic sums.
• However, in the case of ABJM model only the asymptotic contribution can still be written in the harmonic sums basis, while the wrapping corrections part can not.