1998/05/31 by A. L. Larsen, N. Sánchez
Mathematics · Physics and Astronomy · #Antisymmetric tensor #Black Holes and Theoretical Physics #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Equations of motion #Gauge theory #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Non-critical string theory #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Spacetime #String (physics) #String field theory #Torsion (gastropod) #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.58.126002
published as Phys.Rev. D58 (1998) 126002 · 24 pages including 4 postscript figures. Enlarged version including a section on string solutions in 2+1 black hole background. To be published in Phys. Rev. D., December 1998
openalex publication_date 1998/11/19 · arxiv created 1998/11/23 · arxiv updated 2016/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has been known for some time that the SL(2,R) WZWN model reduces to Liouville theory. Here we give a direct and physical derivation of this result based on the classical string equations of motion and the proper string size. This allows us to extract precisely the physical effects of the metric and antisymmetric tensor, respectively, on the exact string dynamics in the SL(2,R) background. The general solution to the proper string size is also found. We show that the antisymmetric tensor (corresponding to conformal invariance) generally gives rise to repulsion, and it precisely cancels the dominant attractive term arising from the metric. Both the sinh-Gordon and the cosh-Gordon sectors of the string dynamics in non-conformally invariant AdS spacetime reduce here to the Liouville equation (with different signs of the potential), while the original Liouville sector reduces to the free wave equation. Only the very large classical string size is affected by the torsion. Medium and small size string behaviors are unchanged. We also find illustrative classes of string solutions in the SL(2,R) background: dynamical closed as well as stationary open spiralling strings, for which the effect of torsion is somewhat like the effect of rotation in the metric. Similarly, the string solutions in the 2+1 BH-AdS background with torsion and angular momentum are fully analyzed.