Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result

Abstract

We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the $sl(2)$ sector of planar $\mathcal{N}=4$ SYM. In particular, we perform explicitly the all-order computation at strong 't Hooft coupling regarding the first (contribution to the) generalised scaling function. Moreover, we compare our asymptotic results with the numerical solutions finding a very good agreement and evaluate numerically the non-asymptotic contributions. Eventually, we illustrate the agreement and prediction on the string side.

references added, typos corrected; Latex file plus one figure

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Cited by in corpus (8)

• Comment on the Scaling Function in AdS4 x CP3
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Scaling function in AdS/CFT from the O(6) sigma model
• The virtual scaling function of AdS/CFT
• Nonperturbative scales in AdS/CFT
• Structure of the string R-matrix
• The integrable O(6) model and the correspondence: checks and predictions
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory