On the Null Vectors in the Spectra of the 2D Integrable Hierarchies

Abstract

We propose an alternative description of the spectrum of local fields in the classical limit of the integrable quantum field theories. It is close to similar constructions used in the geometrical treatment of W-gravities. Our approach provides a systematic way of deriving the null-vectors that appear in this construction. We present explicit results for the case of the A_1^{1}-(m)KdV and the A_2^{2}-(m)KdV hierarchies, different classical limits of 2D CFT's. In the former case our results coincide with the classical limit of the construction of Babelon, Bernard and Smirnov.Some hints about quantization and off-critical treatment are also given.

15 pages, LATEX file, to appear in Phys.Lett.B

References in corpus (3)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Null-vectors in Integrable Field Theory

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• From the braided to the usual Yang-Baxter relation
• Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory
• Exact conserved quantities on the cylinder II: off-critical case
• Non-Local Virasoro Symmetries in the mKdV Hierarchy
• Gauging of Geometric Actions and Integrable Hierarchies of KP Type
• Aspects of Symmetry in Sine-Gordon Theory