Geometrical Loci and CFTs via the Virasoro Symmetry of the mKdV-SG hierarchy: an excursus
Abstract
We will describe the appearance of specific algebraic KdV potentials as a consequence of a requirement on a integro-differential expression. This expression belongs to a class generated by means of Virasoro vector fields acting on the KdV field. The ``almost'' rational KdV fields are described in terms of a geometrical locus of complex points. A class of solutions of this locus has recently appeared as a description of any conformal Verma module without degeneration.
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