Double-logs, Gribov-Lipatov reciprocity and wrapping

Abstract

We study analytical properties of the five-loop anomalous dimension of twist-2 operators at negative even values of Lorentz spin. Following L. N. Lipatov and A. I. Onishchenko, we have found two possible generalizations of double-logarithmic equation, which allow to predict a lot of poles of anomalous dimension of twist-2 operators at all orders of perturbative theory from the known results. Second generalization is related with the reciprocity-respecting function, which is a single-logarithmic function in this case. We have found, that the knowledge of first orders of the reciprocity-respecting function gives all-loop predictions for the highest poles. Obtained predictions can be used for the reconstruction of a general form of the wrapping corrections for twist-2 operators.

17 pages, references added

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Cited by in corpus (7)

• Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
• Analytic continuation of harmonic sums with purely imaginary indices near the integer values
• Anomalous dimensions at small spins
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing