Email this article Free fermions, W-algebras, and isomonodromic deformations
- Authors: Gavrylenko P.G.1,2, Marshakov A.V.1,3,4
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Affiliations:
- Laboratory of Representation Theory and Mathematical Physics, Mathematics Faculty
- Bogolyubov Institute for Theoretical Physics
- Lebedev Physical Institute, RAS
- Institute for Theoretical and Experimental Physics
- Issue: Vol 187, No 2 (2016)
- Pages: 649-677
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/170572
- DOI: https://doi.org/10.1134/S0040577916050044
- ID: 170572
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Abstract
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.
About the authors
P. G. Gavrylenko
Laboratory of Representation Theory and Mathematical Physics, Mathematics Faculty; Bogolyubov Institute for Theoretical Physics
Author for correspondence.
Email: gavrylenko@bitp.kiev.ua
Russian Federation, Moscow; Kiev
A. V. Marshakov
Laboratory of Representation Theory and Mathematical Physics, Mathematics Faculty; Lebedev Physical Institute, RAS; Institute for Theoretical and Experimental Physics
Email: gavrylenko@bitp.kiev.ua
Russian Federation, Moscow; Moscow; Moscow
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