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

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 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 at strong coupling. We explicitly derive the dependence of anomalous dimension on spin for all leading and next-to-leading orders. 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.

Large-spin expansions of GKP strings

“…Alternatively, one may calculate quantum corrections to the AdS 3 GKP-string [36,37]. In a recent paper, the authors of [38] succeeded in calculating all the classical leading and subleading terms of series (1.2) at strong coupling, by introducing an iterative method that can potentially supply all the classical terms at an arbitrary subleading order. The current work extends the method of [38] to examples other than the classic GKP case (I).…”

“…In a recent paper, the authors of [38] succeeded in calculating all the classical leading and subleading terms of series (1.2) at strong coupling, by introducing an iterative method that can potentially supply all the classical terms at an arbitrary subleading order. The current work extends the method of [38] to examples other than the classic GKP case (I). 4 In their original treatment [8], Gubser, Klebanov and Polyakov gave the following formula for the anomalous dimensions of the N = 4 SYM operator that is dual to the R × S 2 closed and folded string (II):…”

“…The series ρ (mm) and ρ (m+1,m) were derived for the first time in [38]. The infinite series of the next-to-next-to-leading coefficients ρ (m+2,m) is derived in section 6.…”

Large-spin and large-winding expansions of giant magnons and single spikes

“…. By the same token, following a program of study initiated in [43], we have computed all the leading, subleading and next-to-subleading coefficients in the large-spin expansion of the anomalous dimensions of twist-2 operators that are dual to long folded strings spinning inside AdS 3 . In [44] the above analysis was applied to strings rotating inside AdS 4 × CP 3 .…”

Large J expansion in ABJM theory revisited

“…Now let's try to expand the elliptic integrals and reverse the series following the ideas of [15]. Using formulas (A.8) and (A.10) from the Appendix A we can represent the energy and the spin (2.16) in the form suitable for expansion:…”