Large-spin expansions of GKP strings

We demonstrate that the large-spin expansion of the energy of Gubser-Klebanov-Polyakov (GKP) strings that rotate in ℝ×S² and AdS₃ can be expressed in terms of Lambert's W-function. We compute the leading, subleading and next-to-subleading series of exponential corrections to the infinite-volume dispersion relation of GKP strings that rotate in ℝ×S². These strings are dual to the long N=4 SYM operators Tr[Φ Z^m Φ Z^J−m]+… and provide their scaling dimensions at strong coupling. We also show that the strings obey a short-long (strings) duality. For the folded GKP strings that spin inside AdS₃ and are dual to twist-2 operators, we confirm the known formulas for the leading and next-to-leading coefficients of their anomalous dimensions and derive the corresponding expressions for the next-to-next-to-leading coefficients