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Communications in Mathematical Physics

, Volume 186, Issue 3, pp 601–648 | Cite as

Null-Vectors in Integrable Field Theory

  • O. Babelon
  • D. Bernard
  • F. A. Smirnov

Abstract:

The form factor bootstrap approach allows to construct the space of local fields in the massive restricted sine-Gordon model. This space has to be isomorphic to that of the corresponding minimal model of conformal field theory. We describe the subspaces which correspond to the Verma modules of primary fields in terms of the commutative algebra of local integrals of motion and of a fermion (Neveu–Schwarz or Ramond depending on the particular primary field). The description of null-vectors relies on the relation between form factors and deformed hyper-elliptic integrals. The null-vectors correspond to the deformed exact forms and to the deformed Riemann bilinear identity. In the operator language, the null-vectors are created by the action of two operators ? (linear in the fermion) and ? (quadratic in the fermion). We show that by factorizing out the null-vectors one gets the space of operators with the correct character. In the classical limit, using the operators ? and ? we obtain a new, very compact, description of the KdV hierarchy. We also discuss a beautiful relation with the method of Whitham.

Keywords

Form Factor Minimal Model Classical Limit Commutative Algebra Conformal Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • O. Babelon
    • 1
  • D. Bernard
    • 2
  • F. A. Smirnov
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes Energies, Laboratoire associé au CNRS, Université Pierre et Marie Curie, Tour 16 1er étage, 4 place Jussieu, 75252 Paris cedex 05, FranceFR
  2. 2.Service de Physique Théorique de Saclay, Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique, F-91191, Gif-sur-Yvette, FranceFR

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