### Abstract

We revisit the computation of the 2-loop correction to the energy of a folded spinning string in AdS5 with an angular momentum J in S^{5} in the scaling limit ln S « 1, J/√λ ln S = fixed. This correction gives the third term in the strong-coupling expansion of the generalized scaling function. The computation, using the AdS light-cone gauge approach developed in our previous paper, is done by expanding the AdS _{5} × S^{5} superstring partition function near the generalized null cusp world surface associated to the spinning string solution. The result corrects and extends the previous conformal gauge result of arXiv:0712.2479 and is found to be in complete agreement with the corresponding terms in the generalized scaling function as obtained from the asymptotic Bethe ansatz in arXiv:0805.4615 (and also partially from the quantum O(6) model and the Bethe ansatz data in arXiv:0809.4952). This provides a highly nontrivial strong coupling comparison of the Bethe ansatz proposal with the quantum AdS _{5} × S^{5} superstring theory, which goes beyond the leading semiclassical term effectively controlled by the underlying algebraic curve. The 2-loop computation we perform involves all the structures in the AdS light-cone gauge superstring action of hep-th/0009171 and thus tests its ultraviolet finiteness and, through the agreement with the Bethe ansatz, its quantum integrability. We do most of the computations for a generalized spinning string solution or the corresponding null cusp surface that involves both the orbital momentum and the winding in a large circle of S^{5}.

Original language | English (US) |
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Article number | 60 |

Journal | Journal of High Energy Physics |

Volume | 2010 |

Issue number | 6 |

DOIs | |

State | Published - 2010 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- AdS-CFT correspondence
- Field theories in lower dimensions

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## Cite this

_{5}× S

^{5}superstring.

*Journal of High Energy Physics*,

*2010*(6), [60]. https://doi.org/10.1007/JHEP06(2010)060