Virasoro constraints in Drinfeld–Sokolov hierarchies

Pavel Safronov ^[1]
1. [1] University of Oxford
  
  University of Oxford
  
  Oxford District, Reino Unido
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 1, 2016, págs. 27-54
Idioma: inglés
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Resumen
- 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.