Speeding Strings

TL;DR

This paper explores the behavior of fast-moving strings in AdS/CFT, showing their worldsheet can be approximated as a perturbation of degenerate solutions, linking string dynamics to Yang-Mills perturbative expansions.

Contribution

It generalizes known classical string solutions related to the Neumann system by analyzing high-velocity limits and connecting the worldsheet perturbation series to Yang-Mills theory.

Findings

Fast string worldsheet approximated as a perturbation of degenerate solutions.

Perturbative expansion in relativistic factor corresponds to Yang-Mills perturbation.

Operators with minimal anomalous dimension relate to trajectories in a combined Neumann system.

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.