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

TL;DR

This paper provides exact solutions for circular strings in 2+1 dimensional de Sitter and anti de Sitter spacetimes, analyzing their properties, equations of state, and semi-classical quantization, revealing distinct mass spectra and state counts.

Contribution

It offers the first exact elliptic function solutions for circular strings in these spacetimes and explores their quantum properties and state spectra.

Findings

Exact elliptic function solutions for circular strings in dS and AdS.

Finite number of states in de Sitter spacetime, infinite in anti de Sitter.

Distinct mass spectra and level spacings for strings in dS and AdS.

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 $\alpha'm^2_{\mbox{dS}}\approx 4n-5H^2\alpha'n^2,\;(n\in N_0),$ 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.