Analytic three-loop Solutions for N=4 SYM Twist Operators

Abstract

We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of twist-two operators. As such we derive the maximally transcendental part of the corresponding three-loop QCD result from the maximal supersymmetric gauge theory in four dimension purely by methods of integrability.

23 pages; v2: references added, appendix A improved

References in corpus (40)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• A semi-classical limit of the gauge/string correspondence
• Transcendentality and Crossing
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Harmonic sums, Mellin transforms and Integrals
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• High energy QCD as a completely integrable model
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Baryon Distribution Amplitudes in QCD
• Integrability of three-particle evolution equations in QCD
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Dressing and Wrapping
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Integrability in QCD and beyond
• Wrapping at four loops in N=4 SYM
• On the highest transcendentality in N=4 SUSY
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• High Energy Asymptotics of Multi--Colour QCD and Exactly Solvable Lattice Models
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Functional BES equation
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Iterative Structure of the N=4 SYM Spin Chain
• Nesting and Dressing
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations

Cited by in corpus (28)

• Four loop twist two, BFKL, wrapping and strings
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Twist-three at five loops, Bethe Ansatz and wrapping
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• The virtual scaling function of AdS/CFT
• Two-loop diagrams in non-relativistic QCD with elliptics
• Analytic solution of the multiloop Baxter equation
• QCD properties of twist operators in the N=6 Chern-Simons theory
• Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• The property of maximal transcendentality: calculation of master integrals
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• Two-Loop Spectroscopy of Short ABJM Operators
• ABJM quantum spectral curve and Mellin transform
• The property of maximal transcendentality: calculation of Feynman integrals
• Baxter equation beyond wrapping
• From weak coupling to spinning strings
• Large-Spin Expansions of GKP Strings
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• The property of maximal transcendentality in the N=4 SYM
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve