Notes on fast moving strings

TL;DR

This paper reviews recent findings on the mechanics of fast moving strings in anti-de Sitter spaces, explores conserved charges, and proposes a generalization linking these charges to operator lengths in field theory.

Contribution

It introduces a generalized relation for conserved charges applicable to arbitrary string solutions and conjectures their role as action variables in classical string dynamics.

Findings

Conserved charges relate to string length in field theory.

A generalization of charge relations for non-rigid solutions.

Proposal that infinite conserved charges form action variables.

Abstract

We review the recent work on the mechanics of fast moving strings in anti-de Sitter space times a sphere and discuss the role of conserved charges. An interesting relation between the local conserved charges of rigid solutions was found in the earlier work. We propose a generalization of this relation for arbitrary solutions, not necessarily rigid. We conjecture that an infinite combination of local conserved charges is an action variable generating periodic trajectories in the classical string phase space. It corresponds to the length of the operator on the field theory side.