Circular strings and multi-strings in de Sitter and anti de Sitter spacetimes

摘要

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'm^2_{\mbox{dS}}\approx 4n-5H^2\alpha'n^2, \;(n\in N_0), and a {\it finite} number of states N_{\mbox{dS}}\approx 0.34/(H^2\alpha') in de Sitter spacetime; m^2_{\mbox{AdS}}\approx H^2n^2 (large n\in N) and N_{\mbox{AdS}}=\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.