Segmented strings and the McMillan map

TL;DR

This paper derives exact elliptic function solutions for closed segmented strings in AdS3, leveraging integrability and the McMillan map, and introduces a discrete evolution rule for bound states of strings and D1-branes.

Contribution

It provides new explicit solutions for string motion in AdS3 and a novel discrete evolution rule for bound states, expanding understanding of integrable string dynamics.

Findings

Exact elliptic function solutions for segmented strings in AdS3.

Reduction of equations to the McMillan map demonstrating integrability.

A discrete evolution rule for bound states of strings and D1-branes.

Abstract

We present new exact solutions describing motions of closed segmented strings in $AdS_3$ in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. We also obtain a discrete evolution rule for the motion in $AdS_3$ of arbitrary bound states of fundamental strings and D1-branes in the test approximation.