The scaling function at strong coupling from the quantum string Bethe equations

Details The scaling function at strong coupling from the quantum string Bethe equations The scaling function at strong coupling from the quantum string Bethe equations

2007-03-14

arxiv.org/abs/hep-th/0703131v1

JHEP 0704:066,2007

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 5 eps figures

Scientific paper

10.1088/1126-6708/2007/04/066

We study at strong coupling the scaling function describing the large spin anomalous dimension of twist two operators in ${\cal N}=4$ super Yang-Mills theory. In the spirit of AdS/CFT duality, it is possible to extract it from the string Bethe Ansatz equations in the $\mathfrak{sl}(2)$ sector of the $\ads$ superstring. To this aim, we present a detailed analysis of the Bethe equations by numerical and analytical methods. We recover several short string semiclassical results as a check. In the more difficult case of the long string limit providing the scaling function, we analyze the strong coupling version of the Eden-Staudacher equation, including the Arutyunov-Frolov-Staudacher phase. We prove that it admits a unique solution, at least in perturbation theory, leading to the correct prediction consistent with semiclassical string calculations.

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