The Multivalued Free-Field Maps of Liouville and Toda Gravities

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 $A_1$ or $A_2$ 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.

47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging to permit Postscript generation, no changes to paper

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Cited by in corpus (9)

• Cosmological solutions, p-branes and the Wheeler-DeWitt equation
• Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras
• An elegant solution of the n-body Toda problem
• Conformal Toda theory with a boundary
• Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
• Canonical BRST Quantisation of Worldsheet Gravities
• Embedding of the Bosonic String into the $W_3$ String
• Negative Screenings in Liouville Theory
• Negative Screenings in Conformal Field Theory and 2D Gravity: The Braiding Matrix