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.Comment: 28 pages, 2 eps figures, LaTeX. v2: typos correcte
