Free fermions, W-algebras, and isomonodromic deformations

Resumo

We consider the theory of multicomponent free massless fermions in two dimensions and use it to construct representations of W-algebras at integer Virasoro central charges. We define the vertex operators in this theory in terms of solutions of the corresponding isomonodromy problem. We use this construction to obtain some new insights into tau functions of the multicomponent Toda-type hierarchies for the class of solutions given by the isomonodromy vertex operators and to obtain a useful representation for tau functions of isomonodromic deformations.