Fine structure of anomalous dimensions in N=4 super Yang-Mills theory

Abstract

Anomalous dimensions of high-twist Wilson operators in generic gauge theories occupy a band of width growing logarithmically with their conformal spin. We perform a systematic study of its fine structure in the autonomous SL(2) subsector of the dilatation operator of planar N=4 super Yang-Mills theory which is believed to be integrable to all orders in 't Hooft coupling. We resort in our study on the framework of the Baxter equation to unravel the properties of the ground state trajectory and the excited trajectories in the spectrum. We use two complimentary approaches in our analysis based on the asymptotic solution of the Baxter equation and on the semiclassical expansion to work out the leading asymptotic expression for the trajectories in the upper and lower part of the band and to find how they are modified by the perturbative corrections.

34 pages; v2: minor corrections, reference added

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• The all loop AdS4/CFT3 Bethe ansatz
• Twist-three at five loops, Bethe Ansatz and wrapping
• The Four Loop QCD Rapidity Anomalous Dimension
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Four loop reciprocity of twist two operators in N=4 SYM
• Strong Coupling Expansion for the Conformal Pomeron/Odderon Trajectories
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Exact Results in Supersymmetric Gauge Theories
• Beyond cusp anomalous dimension from integrability in SYM${}_4$