Analytic solution of the multiloop Baxter equation

Abstract

The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its $sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.

44 pages, v2: references added and typos fixed

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Cited by in corpus (21)

• Five-Loop Anomalous Dimension of Twist-Two Operators
• N=2 Conformal SYM theories at large N
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• Two-loop diagrams in non-relativistic QCD with elliptics
• On wrapping corrections to GKP-like operators
• Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation
• Scaling dimensions at small spin in N=4 SYM theory
• The property of maximal transcendentality: calculation of master integrals
• Riemann $\zeta (3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• ABJM quantum spectral curve and Mellin transform
• The property of maximal transcendentality: calculation of Feynman integrals
• 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
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability