The multivalued free-field maps of Liouville and Toda gravities

1994/01/01 by Arlen Anderson, A. Anderson, B. E. W. Nilsson +5
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Field (mathematics) #Free field #Invariant (physics) #Lie algebra #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Spectral line #hep-th

paper · pdf · doi:10.1016/0550-3213(94)90652-1

published as Nucl.Phys.B430:107-152,1994 · 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging to permit Postscript generation, no changes to paper

openalex publication_date 1994/01/01 · arxiv created 1997/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding A₁ or A₂ Lie algebra. We study the canonical transformations between interacting and free fields using the technique of intertwining operators, giving explicit constructions for the wavefunctions and showing that they are invariant under the corresponding Weyl groups. These explicit constructions also permit a detailed analysis of the operator-state maps and of the nature of the Seiberg bounds.

Citations

• Lectures on 2D gravity and 2D string theory (TASI 1992)
• On the Spectrum and Scattering of W₃ Strings
• Quantum geometry of bosonic strings
• Quantum canonical transformations and integrability. Beyond unitary transformations
• Discrete States in the W₃ String
• A BRST operator for non-critical W-strings
• The geometry of string perturbation theory
• The Low-level Spectrum of the W₃ String