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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• Exciting the GKP string at any coupling
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• Resurgence of the Cusp Anomalous Dimension
• The virtual scaling function of AdS/CFT
• Beyond cusp anomalous dimension from integrability
• Nonperturbative scales in AdS/CFT
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• Generalised scaling at subleading order
• Exact results for the low energy AdS(4)XCP(3) string theory
• Operator with large spin and spinning D3-brane