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

Matteo Beccaria·Gian Fabrizio De Angelis·Valentina Forini
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Abstract

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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Matteo Beccaria, Gian Fabrizio De Angelis, Valentina Forini. 2007-03-14. The scaling function at strong coupling from the quantum string Bethe equations. https://doi.org/10.1088/1126-6708%2F2007%2F04%2F066

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