  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.
