Spiky strings, lightlike Wilson loops, and pp-wave anomaly

Abstract

We consider rigid rotating closed strings with spikes in AdS 5 dual to certain higher twist operators in N = 4 SYM theory. In the limit of large spin when the spikes reach the boundary of AdS 5 , 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 (λ) 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 that 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.

Spiky strings in the SL(2) Bethe Ansatz at strong coupling from AdS/CFT

“…which is the same as the pp-wave limit scaling found at strong coupling in [20,21]. More precisely we obtain…”

“…It turns out that, in the limit of large number of spikes n → ∞, there is an interesting scaling limit in which E+S n 2 , E−S n and J n remain fixed. It was shown in [21] that the solution in this limit is related to a solution in the AdS pp-wave background introduced in [20]. In this paper, by using the found Bethe ansatz solution, it is shown that the same pp-wave like limit can be taken at weak coupling.…”

“…At leading order in large S the spiky string solution touches the boundary of AdS 3 . It was shown [20] that at this order the spiky string solution can be mapped to the folded string solution by a conformal transformation, and thus the all loop energy at leading order in large S is given by…”

New open string solutions inAdS5

“…We extend the solution obtained in [16] in this context to other, more complex solutions. We find solutions ending on two straight light-like lines in the x + direction on the boundary in the pp-wave AdS 5 space, which when translated in the pure AdS 5 look like hyperbolas in a (t, x) plane.…”

On elliptic string solutions in AdS3 and dS3

“…In AdS 3 , a family of interesting solutions, possessing a finite number of singular points, were discovered some years ago [38][39][40][41]. These solutions, which are called spiky strings, are interesting in the framework of AdS/CFT, as they can be related to single trace operators of the dual CFT [38].…”