Anomalous dimensions of high-spin operators beyond the leading order

Abstract

Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading corrections suppressed by powers of the Lorentz spin. We argue that this structure is a manifestation of the `self-tuning' property of the multi-loop anomalous dimensions - in a conformal gauge theory, the anomalous dimension of Wilson operators is a function of their conformal spin which is modified in higher loops by an amount proportional to the anomalous dimension. Making use of the parity property of this function and incorporating the beta-function contribution, we demonstrate the existence of (infinite number of) relations between subleading corrections to the twist-two anomalous dimensions in QCD and its supersymmetric extensions. They imply that the subleading corrections to the anomalous dimensions suppressed by odd powers of the conformal spin can be expressed in terms of the lower-loops corrections suppressed by smaller even powers of the spin. We show that these relations hold true in QCD to all loops in the large beta0 limit. In the N=4 SYM theory, we employ the AdS/CFT correspondence to argue that the same relations survive in the strong coupling regime for higher-twist scalar operators dual to a folded string rotating on the AdS3xS1.

29 pages; v2: minor changes, references added; v3: eqs.(3.25) and (3.26) corrected

References in corpus (3)

• Spinning strings and AdS/CFT duality
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• N=4 SUSY Yang--Mills: three loops made simple(r)

Cited by in corpus (16)

• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• Twist-three at five loops, Bethe Ansatz and wrapping
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The virtual scaling function of AdS/CFT
• Four loop reciprocity of twist two operators in N=4 SYM
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Jet fragmentation and gauge/string duality
• Reciprocity of gauge operators in N=4 SYM
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Magnons and BFKL
• On the short string limit of the folded spinning string in AdS5 x S5
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• On threshold resummation of the longitudinal structure function