Multistring solutions by soliton methods in de Sitter spacetime

Journal Article · Mon Aug 15 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.2754· OSTI ID:7161565

Combes, F; de Vega, H J; Mikhailov, A V; Sanchez, N ^[1]

---

1. Observatoire de Paris, Demirm, Laboratoire Associe au CNRS UA 336, Observatoire de Paris et Ecole Normale Superieure, 61, Avenue de'l'Observatoire 75014 Paris (France) Laboratoire de Physique Theorique et Hautes Energies, Laboratoire associe-CNRS UA280, Universite Paris VI, Tour 16, 1er etage, 4, Place Jussieu, 75252 Paris, Cedex 05 (France) Landau Institute for Theoretical Physics, Russian Academy of Sciences, Ul. Kossyguina 2, 117334 Moscow (Russian Federation)

Exact solutions of the string equations of motion and constraints are systematically constructed in de Sitter spacetime using the dressing method of soliton theory. The string dynamics in de Sitter spacetime is integrable due to the associated linear system. We start from an exact string solution [ital q][sub (0)] and the associated solution of the linear system [Psi][sup (0)]([lambda]), and we construct a new solution [Psi]([lambda]) differing from [Psi][sup (0)]([lambda]) by a rational matrix in [lambda] with at least four poles [lambda][sub 0],1/[lambda][sub 0],[lambda][sub 0][sup *],1/[lambda][sub 0][sup *]. The periodicity condition for closed strings restricts [lambda][sub 0] to discrete values expressed in terms of Pythagorean numbers. Here we explicitly construct solutions depending on (2+1)-spacetime coordinates, two arbitrary complex numbers (the polarization vector''), and two integers ([ital n],[ital m]) which determine the string windings in the space. The solutions are depicted in the hyperboloid coordinates [ital q] and in comoving coordinates with the cosmic time [ital T]. Despite the fact that we have a single world sheet, our solutions describe [ital multiple] (here five) different and independent strings; the world sheet time [tau] turns out to be a multivalued function of [ital T]. (This has no analogue in flat spacetime.) One string is stable (its proper size tends to a constant for [ital T][r arrow][infinity], and its comoving size contracts); the other strings are unstable (their proper sizes blow up for [ital T][r arrow][infinity], while their comoving sizes tend to constants). These solutions (even the stable strings) do not oscillate in time. The interpretation of these solutions and their dynamics in terms of the sinh-Gordon model is particularly enlightening.

• OSTI ID: 7161565
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 50:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
STRING MODELS
SOLITONS
ANALYTICAL SOLUTION
POLARIZATION
SINE-GORDON EQUATION
SPACE-TIME
THREE-DIMENSIONAL CALCULATIONS
COMPOSITE MODELS
EQUATIONS
EXTENDED PARTICLE MODEL
FIELD EQUATIONS
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
QUASI PARTICLES
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)