On analytical perturbative solution of ABJM quantum spectral curve
arXiv:1807.06267 · doi:10.1134/S0040577919020077
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.
22 pages, contribution to CQIS-2017 proceedings, to appear in TMPh. arXiv admin note: text overlap with arXiv:1712.00412. References added
References in corpus (30)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
- Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
- The Bethe ansatz for superconformal Chern-Simons
- The all loop AdS4/CFT3 Bethe ansatz
- An Operator Product Expansion for Polygonal null Wilson Loops
- Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
- On AdS_5 x S^5 String S-matrix
- Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
- Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
- Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
- The Quantum Spectral Curve of the ABJM theory
- Strongly γ-deformed N=4 SYM as an integrable CFT
- Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
- Adjoint BFKL at finite coupling: a short-cut from the collinear limit
- Bi-scalar integrable CFT at any dimension
- Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
- Wronskian Solution for AdS/CFT Y-system
- Hexagonalization of Correlation Functions II: Two-Particle Contributions
- An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
- Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve
- Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
- Exact Correlators on the Wilson Loop in SYM: Localization, Defect CFT, and Integrability
- BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
- The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
- Exploring the spectrum of planar at finite coupling
- Quantum Spectral Curve of -twisted SYM theory and fishnet CFT
- Positivity of hexagon perturbation theory
- ABJM quantum spectral curve and Mellin transform
- Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory