ABJM quantum spectral curve at twist 1: algorithmic perturbative solution

Abstract

We present an algorithmic perturbative solution of ABJM quantum spectral curve at twist 1 in sl(2) sector for arbitrary spin values, which can be applied to, in principle, arbitrary order of perturbation theory. We determined the class of functions -- products of rational functions in spectral parameter with sums of Baxter polynomials and Hurwitz functions -- closed under elementary operations, such as shifts and partial fractions, as well as differentiation. It turns out, that this class of functions is also sufficient for finding solutions of inhomogeneous Baxter equations involved. For the latter purpose we present recursive construction of the dictionary for the solutions of Baxter equations for given inhomogeneous parts. As an application of the proposed method we present the computation of anomalous dimensions of twist 1 operators at six loop order. There is still a room for improvements of the proposed algorithm related to the simplifications of arising sums. The advanced techniques for their reduction to the basis of generalized harmonic sums will be the subject of subsequent paper. We expect this method to be generalizable to higher twists as well as to other theories, such as N=4 SYM.

arXiv comment38 pages

References in corpus (103)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Review of AdS/CFT Integrability: An Overview
• Transcendentality and Crossing
• The N=4 SYM Integrable Super Spin Chain
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• The su(2|2) Dynamic S-Matrix
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Integrability for the Full Spectrum of Planar AdS/CFT
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Quantum spectral curve for AdS_5/CFT_4
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Thermodynamic Bubble Ansatz
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• The all loop AdS4/CFT3 Bethe ansatz
• An Operator Product Expansion for Polygonal null Wilson Loops
• Revisiting parton evolution and the large-x limit
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• On AdS_5 x S^5 String S-matrix
• One-point Functions in Defect CFT and Integrability
• Anomalous dimensions of high-spin operators beyond the leading order
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Integrable Wilson loops
• One-point Functions in AdS/dCFT from Matrix Product States
• Tessellating cushions: four-point functions in N=4 SYM
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• The Quantum Spectral Curve of the ABJM theory
• Gluing Ladders into Fishnets
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Strongly γ-deformed N=4 SYM as an integrable CFT
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Integrability of Conformal Fishnet Theory
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Exact Slope and Interpolating Functions in ABJM Theory
• OPE for all Helicity Amplitudes
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Solving the AdS/CFT Y-system
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Yangian Symmetry for Fishnet Feynman Graphs
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Bi-scalar integrable CFT at any dimension
• Structure constants at wrapping order
• Conformal algebra: R-matrix and star-triangle relation
• One-loop one-point functions in gauge-gravity dualities with defects
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Wronskian Solution for AdS/CFT Y-system
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Quark--anti-quark potential in N=4 SYM
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• QCD Pomeron from AdS/CFT Quantum Spectral Curve
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Octagons I: Combinatorics and Non-Planar Resummations
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• The Holographic Fishchain
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Continuum limit of fishnet graphs and AdS sigma model
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• Three-point correlator of twist-2 operators in BFKL limit
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• On the Exact Interpolating Function in ABJ Theory
• Strong coupling results from the numerical solution of the quantum spectral curve
• On wrapping corrections to GKP-like operators
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• QCD properties of twist operators in the N=6 Chern-Simons theory
• Positivity of hexagon perturbation theory
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Exact scattering amplitudes in conformal fishnet theory
• Hexagon POPE: effective particles and tree level resummation
• Discontinuity relations for the AdS(4)/CFT(3) correspondence
• The property of maximal transcendentality: calculation of Feynman integrals
• ABJM quantum spectral curve and Mellin transform
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• ABJM flux-tube and scattering amplitudes

Cited by in corpus (2)

• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Analytic continuation of harmonic sums with purely imaginary indices near the integer values