Infinitely many strings in de Sitter spacetime: expanding and oscillating elliptic function solutions.

DOI10.1016/0550-3213(94)90643-2zbMATH Open1049.81616arXivhep-th/9312115OpenAlexW3106060288MaRDI QIDQ1967533

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Publication date: 6 March 2000

Published in: (Search for Journal in Brave)

Abstract: The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {it infinitely many} (different and independent) strings. The world-sheet time $au$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(dotS>0)$: $Eeq0$ even at $S=0$, $E$ decreases for small $S$ and increases $proptohspace*-1mmS$ for large $S$. For an oscillating string $(0leqSleq{S}_{max})$, the average energy $<E>$ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.

Full work available at URL: https://arxiv.org/abs/hep-th/9312115

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