Segmented Strings in $Ad{S}_3$

Abstract

We study segmented strings in flat space and in $Ad{S}_3$. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In $Ad{S}_3$, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an $Ad{S}_2$ subspace of $Ad{S}_3$. 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 $Ad{S}_3$ and find an unexpected quasi-periodic behavior. We also work out a WKB analysis of quantum states of yo-yo strings in $Ad{S}_3$ and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.

arXiv comment38 pages, 5 figures

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Cited by in corpus (10)

• $p$-adic AdS/CFT
• Chaotic strings in AdS/CFT
• Evolution of segmented strings
• Dynamical AdS strings across horizons
• Segmented strings and the McMillan map
• Gravitating spinning strings in AdS${}_3$
• Mass and spin for classical strings in $d{S}_3$
• The SU(2) Lie-Poisson Algebra and its Descendants
• Relativistic membrane solutions in AdS${}_4$
• The spectral curve of segmented strings