Segmented Strings in $AdS_3$

TL;DR

This paper explores classical segmented string dynamics in flat space and $AdS_3$, revealing a quasi-periodic behavior in $AdS_3$ and analyzing quantum states with a WKB approach, highlighting new geometric and quantum features.

Contribution

It introduces a novel description of segmented strings in $AdS_3$ using null geodesics and analyzes their classical and quantum properties, including collision outcomes and state spectra.

Findings

Quasi-periodic behavior of segmented strings in $AdS_3$

Collision dynamics governed by causality considerations

Logarithmic term in quantum state analysis of yo-yo strings

Abstract

We study segmented strings in flat space and in $AdS_3$. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In $AdS_3$, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an $AdS_2$ subspace of $AdS_3$. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We study several examples of closed segmented strings in $AdS_3$ and find an unexpected quasi-periodic behavior. We also work out a WKB analysis of quantum states of yo-yo strings in $AdS_3$ and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.