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

TL;DR

This paper analyzes the large spin behavior of anomalous dimensions of operators in N=4 SYM using semi-classical string solutions, deriving explicit spin dependence and confirming reciprocity relations at strong coupling.

Contribution

It provides a detailed derivation of anomalous dimension dependence on spin at strong coupling and introduces an iteration method to obtain all terms in the large spin expansion.

Findings

Explicit spin dependence of anomalous dimensions at strong coupling

Verification of reciprocity relation for large spin operators

Duality relation between long and short strings

Abstract

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.