Drinfeld-Sokolov层次中的Virasoro约束
Virasoro constraints in Drinfeld-Sokolov hierarchies
摘要：
我们描述了Virasoro约束的广义Drinfeld-Sokolov层次的几何理论。通过给出复曲线上的主丛以及无穷远处希格斯场的数据，简洁地描述了Drinfeld-Sokolov方程的解.这些族的弦解被定义为在一定的李代数作用下具有大稳定子的点。我们的特点是主丛来自弦的解决方案，那些拥有连接兼容的希格斯场在无穷远。我们证明了弦解的τ函数满足二阶微分方程，推广了二维量子引力的Virasoro约束。
英文摘要：
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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