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

H. J. de Vega, A. L. Larsen, N. Sánchez

Submitted on 10 April 1995


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 αmdS24n5H2αn2,(nN0), and a {\it finite} number of states NdS0.34/(H2α) in de Sitter spacetime; mAdS2H2n2 (large nN) and NAdS= 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.


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