PREPRINT
CFE79634-B5DC-4DC0-8DD1-26B2FF0B97FA

# Circular Strings and Multi-Strings in de Sitter and Anti de Sitter Spacetimes

H. J. de Vega, A. L. Larsen, N. Sánchez
arXiv:hep-th/9504050

Submitted on 10 April 1995

## Abstract

The exact general solution of circular strings in $2+1$ dimensional de Sitter spacetime is described completely in terms of elliptic functions. The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. This has no analogue in flat spacetime. The circular strings are either oscillating ("stable") or indefinitely expanding ("unstable"). We then compute the {\it exact} equation of state of circular strings in the $2+1$ dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. We finally perform a semi-classical quantization of the oscillating circular strings. We find the mass formula ${\alpha }^{\prime }{m}_{\text{dS}}^{2}\approx 4n-5{H}^{2}{\alpha }^{\prime }{n}^{2},\phantom{\rule{0.278em}{0ex}}\left(n\in {N}_{0}\right),$ and a {\it finite} number of states ${N}_{\text{dS}}\approx 0.34/\left({H}^{2}{\alpha }^{\prime }\right)$ in de Sitter spacetime; ${m}_{\text{AdS}}^{2}\approx {H}^{2}{n}^{2}$ (large $n\in N$) and ${N}_{\text{AdS}}=\mathrm{\infty }$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime.

## Preprint

Comment: Latex, 19 pages + 6 figures and 3 tables (not included). To appear in "New Developments in string gravity and physics at the Planck energy scale" (World Scientific, Singapore, 1995)

Subjects: High Energy Physics - Theory; Astrophysics; General Relativity and Quantum Cosmology