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arXiv · 1302.3540

Virasoro constraints in Drinfeld-Sokolov hierarchies

Pavel Safronov
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Abstract

We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a principal bundle on a complex curve together with the data of a Higgs field near infinity. String solutions for these hierarchies are defined as points having a big stabilizer under a certain Lie algebra action. We characterize principal bundles coming from string solutions as those possessing connections compatible with the Higgs field near infinity. We show that tau-functions of string solutions satisfy second-order differential equations generalizing the Virasoro constraints of 2d quantum gravity.

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BibTeXRIS

Pavel Safronov. 2013-02-14. Virasoro constraints in Drinfeld-Sokolov hierarchies. https://doi.org/10.1007/s00029-015-0182-1

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