Speeding Strings

TL;DR

The work develops a controlled ultrarelativistic (fast-string) regime for strings in AdS5×S5, tying large-charge operators in N=4 SYM to null-surface limits Σ(0) equipped with a σ-label. It shows that the minimal one-loop anomalous dimension at fixed charges is captured by periodic trajectories of a gauged Neumann system, equivalently the product of two Neumann systems for AdS5 and S5, and it outlines both exact-worldsheet constructions and the integrability structure behind these solutions. The paper also analyzes off-diagonal charges, gauge freedom, and degenerations of periodic tori, providing a comprehensive framework for connecting YM data (λ/J^2 expansions) to semiclassical string dynamics with a λ-family of worldsheets. Overall, it offers a concrete dynamical model (gauged Neumann system) and a route to exact string solutions that illuminate the AdS/CFT correspondence in the high-spin/high-R regime and its perturbative and strong-coupling connections.

Abstract

There is a class of single trace operators in ${\cal N}=4$ Yang-Mills theory which are related by the AdS/CFT correspondence to classical string solutions. Interesting examples of such solutions corresponding to periodic trajectories of the Neumann system were studied recently. In our paper we study a generalization of these solutions. We consider strings moving with large velocities. We show that the worldsheet of the fast moving string can be considered as a perturbation of the degenerate worldsheet, with the small parameter being the relativistic factor $\sqrt{1-v^2}$. The series expansion in this relativistic factor should correspond to the perturbative expansion in the dual Yang-Mills theory. The operators minimizing the anomalous dimension in the sector with given charges correspond to periodic trajectories in the mechanical system which is closely related to the product of two Neumann systems.