Exact integrability of strings in [ital D]-dimensional de Sitter spacetime

Journal Article · Thu Apr 15 00:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.3394· OSTI ID:6656011

de Vega, H J ^[1]; Sanchez, N ^[2]

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1. Laboratoire de Physique Theorique et Hautes Energies (LPhTHE), Universite Paris VI, tour 16 , 1 er etage, 4 Place Jussieu, F-75252 Paris CEDEX 05 (France)
2. DEMIRM, Observatoire de Paris, Section de Meudon, 92195 Meudon Principal CEDEX (France)

We show the complete integrability of the string propagation in [ital D]-dimensional de Sitter spacetime. We find that the string equations of motion, which correspond to a noncompact O([ital D],1)-symmetric [sigma] model, plus the string constraints, are equivalent to a generalized sinh-Gordon equation. In [ital D]=2 this is the Liouville equation, in [ital D]=3 this is the standard sinh-Gordon equation, and in [ital D]=4 this equation is related to the [ital B][sub 2] Toda model. We show that the presence of instability is a general exact feature of strings in de Sitter space, as a direct consequence of the strong instability of the generalized sinh-Gordon Hamiltonian (which is unbounded from below), irrespective of any approximative scheme. We exhibit Baecklund transformations for this generalized sinh-Gordon equation, which relate expanding and shrinking string solutions. We find all classical solutions in [ital D]=2 and physically analyze them. In [ital D]=3 and [ital D]=4, we find the asymptotic behaviors of the solutions in the instability regime. The exact solutions exhibit asymptotically all the characteristic features of string instability: namely, the logarithmic dependence of the cosmic time [ital u] on the world sheet time [tau] for [ital u][r arrow][plus minus][infinity], the stretching (or the shrinking) of the proper string size, and the proportionality between [tau] and the conformal time.

• OSTI ID: 6656011
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 47:8; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
STRING MODELS
SPACE-TIME
EQUATIONS OF MOTION
FOUR-DIMENSIONAL CALCULATIONS
GRAVITATIONAL WAVES
HAMILTONIANS
HUBBLE EFFECT
SIGMA MODEL
SINE-GORDON EQUATION
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
UNIVERSE
BOSON-EXCHANGE MODELS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
EXTENDED PARTICLE MODEL
FIELD EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PERIPHERAL MODELS
QUANTUM OPERATORS
QUARK MODEL
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)