Toward an Analytic Perturbative Solution for the Abjm Quantum Spectral Curve

• Published in: Theoretical and mathematical physics Vol. 198; no. 2; pp. 256 - 270
• Main Authors: Lee, R. N., Onishchenko, A. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.02.2019; Springer Nature B.V
• Subjects: Applications of Mathematics; Difference equations; Hypergeometric functions; Mathematical analysis; Mathematical and Computational Physics; Operators (mathematics); Physics; Physics and Astronomy; Spectra; Supersymmetry; Theoretical; Yang-Mills theory; Baxter equation; quantum spectral curve; spin chain; ABJM model; anomalous dimension
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577919020077

We recently showed how nonhomogeneous second-order difference equations that appear in describing the ABJM quantum spectral curve can be solved using a Mellin space technique. In particular, we provided explicit results for anomalous dimensions of twist-1 operators in the sl(2) sector at arbitrary spin values up to the four-loop order. We showed that the obtained results can be expressed in terms of harmonic sums with additional factors in the form of a fourth root of unity, and the maximum transcendentality principle therefore holds. Here, we show that the same result can also be obtained by directly solving the mentioned difference equations in the space of the spectral parameter u. The solution involves new highly nontrivial identities between hypergeometric functions, which can have various applications. We expect that this method can be generalized both to higher loop orders and to other theories, such as the N=4 supersymmetric Yang–Mills theory.