Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-08-04
Nucl.Phys.B827:565-606,2010
Physics
High Energy Physics
High Energy Physics - Theory
44 pages, v2: references added and typos fixed
Scientific paper
10.1016/j.nuclphysb.2009.10.030
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.
Beccaria Matteo
Belitsky Andrei V.
Kotikov Anatoly V.
Zieme Stefan
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