Generalized Scaling Function at Strong Coupling

TL;DR

This paper computes the energy of folded spinning strings in AdS_5 x S^5 at strong coupling with 2-loop accuracy, revealing finite results in certain limits and developing methods applicable to systematic expansions at various coupling regimes.

Contribution

It introduces a method to compute string energies at strong coupling with high precision and extends the analysis to arbitrary orders in perturbation theory.

Findings

Finite energy results in the l-> 0 limit due to massive cancellations.

Reproduction of known results at leading order from sigma model.

Development of a systematic expansion method for strong and weak coupling regimes.

Abstract

We considered folded spinning string in AdS_5 x S^5 background dual to the Tr(D^S Phi^J) operators of N=4 SYM theory. In the limit S,J-> \infty and l=pi J/\sqrt\lambda\log S fixed we compute the string energy with the 2-loop accuracy in the worldsheet coupling \sqrt\lambda from the asymptotical Bethe ansatz. In the limit l-> 0 the result is finite due to the massive cancelations with terms coming from the conjectured dressing phase. We also managed to compute all leading logarithm terms l^{2m}\log^n l/\lambda^n/2 to an arbitrary order in perturbation theory. In particular for m=1 we reproduced results of Alday and Maldacena computed from a sigma model. The method developed in this paper could be used for a systematic expansion in 1/\sqrt\lambda and also at weak coupling.