Large spin behavior of anomalous dimensions and short-long strings duality

Details Large spin behavior of anomalous dimensions and short-long strings duality Large spin behavior of anomalous dimensions and short-long strings duality

2010-12-27

arxiv.org/abs/1012.5580v3

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 1 figure, comments and references added

Scientific paper

We are considering the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in $AdS_5$. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the space-time spin. We explicitly derive the dependence of anomalous dimension on spin for all leading and next-to-leading orders at strong coupling. We develop an iteration procedure which, in principle, allows to derive all terms in the large spin expansion of the anomalous scaling dimension of twist two operators. Our string theory results are consistent with the conjectured "reciprocity" relation, which has been verified to hold in perturbation theory up to five loops in N=4 SYM. We also derive a duality relation between long and short strings.

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