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

TL;DR

This paper numerically tests the AdS/CFT correspondence by analyzing high-spin operators in N=4 SYM, confirming predictions at strong coupling and providing new numerical insights into the cusp anomaly.

Contribution

It numerically verifies the AdS/CFT correspondence for high-spin operators by solving an integral equation and comparing results with string theory predictions.

Findings

Strong coupling results match string theory predictions with high accuracy.

Numerical prediction for the third term in the strong coupling expansion.

Confirmation of the AdS/CFT correspondence for high-spin operators.

Abstract

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.