### 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) |
---|---|

Article number | 60 |

Journal | Journal of High Energy Physics |

Volume | 2010 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 2010 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

_{5}× S

^{5}superstring.

*Journal of High Energy Physics*,

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

}

_{5}× S

^{5}superstring',

*Journal of High Energy Physics*, vol. 2010, no. 6, 60. https://doi.org/10.1007/JHEP06(2010)060

**Generalized scaling function from light-cone gauge AdS _{5} × S^{5} superstring.** / Giombi, S.; Ricci, R.; Roiban, R.; Tseytlin, A. A.; Vergu, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized scaling function from light-cone gauge AdS 5 × S5 superstring

AU - Giombi, S.

AU - Ricci, R.

AU - Roiban, R.

AU - Tseytlin, A. A.

AU - Vergu, C.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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 S5 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 × S5 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 × S5 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 S5.

AB - 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 S5 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 × S5 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 × S5 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 S5.

UR - http://www.scopus.com/inward/record.url?scp=84856366890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856366890&partnerID=8YFLogxK

U2 - 10.1007/JHEP06(2010)060

DO - 10.1007/JHEP06(2010)060

M3 - Article

AN - SCOPUS:84856366890

VL - 2010

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 6

M1 - 60

ER -

_{5}× S

^{5}superstring. Journal of High Energy Physics. 2010 Jan 1;2010(6). 60. https://doi.org/10.1007/JHEP06(2010)060