Virasoro constraints in Drinfeld-Sokolov hierarchies
Algebraic Geometry
2016-01-19 v2 Mathematical Physics
math.MP
Representation Theory
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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Cite
@article{arxiv.1302.3540,
title = {Virasoro constraints in Drinfeld-Sokolov hierarchies},
author = {Pavel Safronov},
journal= {arXiv preprint arXiv:1302.3540},
year = {2016}
}
Comments
28 pages