Strong-coupling expansion of cusp anomaly from quantum superstring

Radu Roiban, Arkady A. Tseytlin

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98 Scopus citations


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 languageEnglish (US)
Article number016
JournalJournal of High Energy Physics
Issue number11
StatePublished - Nov 1 2007

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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