A Test of the AdS/CFT Correspondence Using High-Spin Operators

Details A Test of the AdS/CFT Correspondence Using High-Spin Operators A Test of the AdS/CFT Correspondence Using High-Spin Operators

2006-11-13

arxiv.org/abs/hep-th/0611135v2

Phys.Rev.Lett.98:131603,2007

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 1 figure; added references, corrected typos

Scientific paper

10.1103/PhysRevLett.98.131603

In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM theory. We study numerically the integral equation derived in hep-th/0610251, which implements a resummation of the perturbative expansion, and find a smooth function that approaches the asymptotic form predicted by string theory. In fact, the two leading terms at strong coupling match with high accuracy the results obtained for the semiclassical folded string spinning in $AdS_5$. This constitutes a remarkable confirmation of the AdS/CFT correspondence for high-spin operators, and equivalently for the cusp anomaly of a Wilson loop. We also make a numerical prediction for the third term in the strong coupling series.

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