Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

Abstract

We 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. The string equation of state has the perfect fluid form $P=(\gamma -1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $\gamma$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(\pi H{\alpha }^{\prime }),C$ being the Casimir operator, $C=-L_{\mu \nu }{L}^{\mu \nu },$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find $α'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),$ and a {\it finite} number of states $N_{\mbox{dS}}\approx 0.17/(H^2α')$ in de Sitter spacetime; $m^2_{\mbox{AdS}}\approx 4H^2n^2$ (large $n\in N_0$) and $N_{\mbox{AdS}}=\infty$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.

Latex, 26 pages + 2 tables and 5 figures that can be obtained from the authors on request. DEMIRM-Obs de Paris-94049

References in corpus (7)

• Mass Spectrum of Strings in Anti de Sitter Spacetime
• Strings Propagating in the 2+1 Dimensional Black Hole Anti de Sitter Spacetime
• Multi-String Solutions by Soliton Methods in De Sitter Spacetime
• Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions
• Back Reaction of Strings in Self-Consistent String Cosmology
• Strings in Cosmological and Black Hole Backgrounds: Ring Solutions
• Exact String Solutions in 2+1-Dimensional De Sitter Spacetime

Cited by in corpus (65)

• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Matching Higher Conserved Charges for Strings and Spins
• Spinning strings and AdS/CFT duality
• Circular Semiclassical String Solutions on AdS_5 x S_5
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Semiclassical quantization of superstrings: AdS_5 x S^5 and beyond
• Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes
• An action variable of the sine-Gordon model
• Mass Spectrum of Strings in Anti de Sitter Spacetime
• Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
• Spinning Pulsating String Solitons in AdS_5 x S^5
• Rotating Strings in Confining AdS/CFT Backgrounds
• Circular Semiclassical String solutions on Confining AdS/CFT Backgrounds
• New Classes of Exact Multi-String Solutions in Curved Spacetimes
• Quantum String Dynamics in the conformal invariant SL(2,R) WZWN Background: Anti-de Sitter Space with Torsion
• QFT, String Temperature and the String Phase of De Sitter Space-time
• Improved Stability for Pulsating Multi-Spin String Solitons
• Novel Explicit Multi Spin String Solitons in AdS(5)
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Multi-spin string solutions in AdS Black Hole and confining backgrounds
• On the propagator of a scalar field in AdS x S and in its plane wave limit
• Pulsating strings on $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Large Spin Strings in AdS_3
• Exact String Solutions in Nontrivial Backgrounds
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Pulsating Strings With Angular Momenta
• Quantum Coherent String States in AdS_3 and SL(2,R) WZWN Model
• Planetoid strings : solutions and perturbations
• Plane wave limit of local conserved charges
• Quantum Discrete Levels of the Universe from the Early Trans-Planckian Vacuum to the Late Dark Energy
• Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
• Orbit method quantization of the AdS${}_2$ superparticle
• Massless Cosmic Strings in Expanding Universe
• Entanglement Entropy in the $\sigma$-Model with the de Sitter Target Space
• Rotating and Orbiting Strings in the Near-Horizon Brane Backgrounds
• STRINGS IN A WORMHOLE BACKGROUND
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• New Quantum Phase of the Universe before Inflation and its Cosmological and Dark Energy Implications
• Advances in String Theory in Curved Backgrounds: A Synthesis Report
• Open String Fluctuations in AdS with and without Torsion
• Quantum Trans-Planckian Physics inside Black Holes and its Spectrum
• Spinning Strings on Deformed AdS_5 x T^{1,1} with NS B-field
• Semiclassical (Quantum Field Theory) and Quantum (String) de Sitter Regimes: New Results
• Spiky strings in de Sitter space
• New Coherent String States and Minimal Uncertainty in WZWN Models
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Microscopic formulation of the S-matrix in AdS/CFT
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• Quantizing Strings in de Sitter Space
• Circular strings, wormholes and minimum size
• Mass and spin for classical strings in $d{S}_3$
• Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions
• Semiclassical (QFT) and Quantum (String) anti - de Sitter Regimes: New Results
• Spinning strings: $\lambda$-deformation and non-Abelian T-dual limit
• Logarithmic correction to scaling for multi-spin strings in the AdS_5 black hole background
• Advances in String Theory in Curved Space Times
• Pulsating Strings in Deformed Backgrounds
• Tunnelling of Pulsating Strings in Deformed Minkowski Spacetime
• Cherenkov Gravitational Radiation During the Radiation Era
• Circular strings in Kerr-$Ad{S}_5$ black holes
• Circular Strings and Multi-Strings in de Sitter and Anti de Sitter Spacetimes