### Abstract

We consider the world surface in AdS _{5} that ends on two intersecting null lines at the boundary. The corresponding superstring partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric gauge theory and thus determines the cusp anomaly function f() of the gauge coupling or the string tension λ/2π. The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a _{0} = 1) and in arXiv:0707.4254 (a _{1} = - 3 ln 2). Here we find that the 2-loop coefficient is a _{2} = -K where K is the Catalan's constant. This is in agreement (expected on the general grounds) with the previous results for f() as the coefficient of ln S term in the energy of the closed spinning string in AdS _{5}. The string theory value for a _{2} is in agreement with the numerical result in hep-th/0611135 and the recent analytic result in arXiv:0708.3933 for the coefficients in strong-coupling Ssolution of the BES equation. We explicitly verify the cancellation of all 2-loop logarithmic divergences thus demonstrating the quantum consistency of the AdS _{5}×S ^{5} superstring action at this order. We also discuss the structure of the three and higher string loop corrections to the cusp anomaly function giving a 2d QFT diagrammatic interpretation to the result of arXiv:0708.3933 for the solution of the BES equation following from the Bethe ansatz prescription for the spectrum of the theory.

Original language | English (US) |
---|---|

Article number | 016 |

Journal | Journal of High Energy Physics |

Volume | 2007 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2007*(11), [016]. https://doi.org/10.1088/1126-6708/2007/11/016

}

*Journal of High Energy Physics*, vol. 2007, no. 11, 016. https://doi.org/10.1088/1126-6708/2007/11/016

**Strong-coupling expansion of cusp anomaly from quantum superstring.** / Roiban, Radu; Tseytlin, Arkady A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong-coupling expansion of cusp anomaly from quantum superstring

AU - Roiban, Radu

AU - Tseytlin, Arkady A.

PY - 2007/11/1

Y1 - 2007/11/1

N2 - We consider the world surface in AdS 5 that ends on two intersecting null lines at the boundary. The corresponding superstring partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric gauge theory and thus determines the cusp anomaly function f() of the gauge coupling or the string tension λ/2π. The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a 0 = 1) and in arXiv:0707.4254 (a 1 = - 3 ln 2). Here we find that the 2-loop coefficient is a 2 = -K where K is the Catalan's constant. This is in agreement (expected on the general grounds) with the previous results for f() as the coefficient of ln S term in the energy of the closed spinning string in AdS 5. The string theory value for a 2 is in agreement with the numerical result in hep-th/0611135 and the recent analytic result in arXiv:0708.3933 for the coefficients in strong-coupling Ssolution of the BES equation. We explicitly verify the cancellation of all 2-loop logarithmic divergences thus demonstrating the quantum consistency of the AdS 5×S 5 superstring action at this order. We also discuss the structure of the three and higher string loop corrections to the cusp anomaly function giving a 2d QFT diagrammatic interpretation to the result of arXiv:0708.3933 for the solution of the BES equation following from the Bethe ansatz prescription for the spectrum of the theory.

AB - We consider the world surface in AdS 5 that ends on two intersecting null lines at the boundary. The corresponding superstring partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric gauge theory and thus determines the cusp anomaly function f() of the gauge coupling or the string tension λ/2π. The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a 0 = 1) and in arXiv:0707.4254 (a 1 = - 3 ln 2). Here we find that the 2-loop coefficient is a 2 = -K where K is the Catalan's constant. This is in agreement (expected on the general grounds) with the previous results for f() as the coefficient of ln S term in the energy of the closed spinning string in AdS 5. The string theory value for a 2 is in agreement with the numerical result in hep-th/0611135 and the recent analytic result in arXiv:0708.3933 for the coefficients in strong-coupling Ssolution of the BES equation. We explicitly verify the cancellation of all 2-loop logarithmic divergences thus demonstrating the quantum consistency of the AdS 5×S 5 superstring action at this order. We also discuss the structure of the three and higher string loop corrections to the cusp anomaly function giving a 2d QFT diagrammatic interpretation to the result of arXiv:0708.3933 for the solution of the BES equation following from the Bethe ansatz prescription for the spectrum of the theory.

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U2 - 10.1088/1126-6708/2007/11/016

DO - 10.1088/1126-6708/2007/11/016

M3 - Article

AN - SCOPUS:36849024845

VL - 2007

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 016

ER -