Strong Coupling Expansion of Cusp Anomalous Dimension in Planar N=4 Supersymmetric Yang-Mills Theory

LPT, Orsay

Fri, Sep. 21st 2007, 11:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

The cusp anomalous dimension is an important and ubiquitous observable in four dimensional gauge theories, ranging from QCD to maximally supersymmetric N=4 Yang-Mills theory (SYM). In particular, it governs the scaling behavior of various gauge invariant quantities, a priori unrelated. The cusp anomalous dimension is a function of the gauge coupling only and its weak coupling expansion is known up to four loops in planar N=4 SYM. At strong coupling, assuming the AdS/CFT correspondence, the cusp anomaly can be obtained from the semiclassical expansion of the energy of a folded string rotating in the AdS3 part of the target space; the strong coupling expansion of the cusp anomaly derived from string theory is known recently up to two loops. \par
One year ago, Beisert, Eden and Staudacher proposed a way to compute the cusp anomaly, at any value of the coupling constant in the planar limit, as part of the solution to an integral equation (BES equation). This equation relies on the assumption that integrability, observed in N=4 SYM at weak coupling, survives to all orders in perturbation theory and matches strong coupling integrable structures previously identified on the string theory side. After a brief introduction to the subject, we shall present the strong coupling expansion of the cusp anomaly derived from the BES equation and discuss its properties.