Spiky strings, light-like Wilson loops and pp-wave anomaly

TL;DR

This paper explores the relationship between spiky rotating strings in AdS5, Wilson loops, and anomalies in N=4 SYM, revealing connections between string configurations, conformal transformations, and the cusp and pp-wave anomalies.

Contribution

It introduces a novel link between spiky string solutions, pp-wave backgrounds, and Wilson loop anomalies, providing new insights into the AdS/CFT correspondence and gauge theory behavior.

Findings

Energy of spiky strings relates to the same function f(lambda) as cusp anomaly.

Identifies a pp-wave anomaly matching the cusp anomaly at lowest order.

Discovers new open string solutions ending on light-like Wilson lines.

Abstract

We consider rigid rotating closed strings with spikes in AdS5 dual to certain higher twist operators in N=4 SYM theory. In the limit of large spin when the spikes reach the boundary of AdS5, the solutions with different numbers of spikes are related by conformal transformations, implying that their energy is determined by the same function of the `t Hooft coupling f(lambda) that appears in the anomalous dimension of twist 2 operators or in the cusp anomaly. In the limit when the number of spikes goes to infinity, we find an equivalent description in terms of a string moving in an AdS pp-wave background. From the boundary theory point of view, the corresponding description is based on the gauge theory living in a 4d pp-wave space. Then, considering a charge moving at the speed of light, or a null Wilson line, we find that the integrated energy momentum tensor has a logarithmic UV divergence whose coefficient we call the "pp-wave anomaly". The AdS/CFT correspondence implies that, for N=4 SYM, this pp-wave anomaly should have the same value as the cusp anomaly. We verify this at lowest order in SYM perturbation theory. As a side result of our string theory analysis, we find new open string solutions in the Poincare patch of the standard AdS space which end on a light-like Wilson line and also in two parallel light-like Wilson lines at the boundary.