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

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

1998-06-11

arxiv.org/abs/hep-th/9806090v1

Phys.Lett. B430 (1998) 109-119

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/S0370-2693(98)00480-8

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.

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