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

Abstract

We consider 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 AdS5. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the spacetime spin. We explicitly derive the coefficients in the large spin expansion of the anomalous dimension in the leading ln nS/Sn and next-to-leading ln nS/Sn + 1 orders. We develop an iteration procedure which, in principle, allows us 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.