On analytical perturbative solution of ABJM quantum spectral curve

TL;DR

This paper presents an alternative direct spectral parameter method for solving ABJM quantum spectral curve equations, revealing new identities between hypergeometric functions and potentially simplifying higher-loop calculations.

Contribution

It introduces a direct spectral parameter solution approach for ABJM quantum spectral curve equations, complementing Mellin space techniques and uncovering new hypergeometric identities.

Findings

Explicit solutions for anomalous dimensions up to four loops.

Identification of new hypergeometric identities.

Potential for generalization to higher loops and other theories.

Abstract

Recently we showed how non-homogeneous second-order difference equations appearing within ABJM quantum spectral curve description could be solved using Mellin space technique. In particular we provided explicit results for anomalous dimensions of twist 1 operators in sl(2) sector at arbitrary spin values up to four loop order. It was shown that the obtained results may be expressed in terms of harmonic sums decorated by fourth root of unity factors, so that maximum transcendentality principle holds. In this note we show that the same result could be also obtained by direct solution of the mentioned equations in spectral parameter u-space. The solution involves new highly nontrivial identities between hypergeometric functions, which may have various other applications. We expect this method to be more easily generalizable to higher loop orders as well as to other theories, such as N=4 SYM.