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

Beccaria, M., De Angelis, G. F. and Forini, V. ORCID: 0000-0001-9726-1423 (2007). The scaling function at strong coupling from the quantum string Bethe equations. Journal of High Energy Physics, 2007, 066.. doi: 10.1088/1126-6708/2007/04/066

Abstract

We study at strong coupling the scaling function describing the large spin anomalous dimension of twist two operators in Script 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 fraktur sfraktur l(2) sector of the AdS5 × S5 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.

Publication Type: Article
Publisher Keywords: integrable quantum field theory, integrable spin chains (vertex models), quantum integrability (Bethe ansatz)
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/19736
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