Segal-Sugawara结构的几何实现
Geometric Realization of the Segal--Sugawara Construction
摘要：
我们将顶点代数的局部化技术应用于Virasoro代数在仿射Kac-Moody代数上的“内部”作用的Segal-Sugawara构造。其结果是将扭曲的微分算子从曲线的模提升到具有丛的曲线的模，具有任意的装饰和复杂的扭曲。这种构造给出了一种统一的方法来处理描述变化曲线上丛的模空间几何的一系列现象：非阿贝尔θ函数上的KZB方程和热核，它们的临界能级极限给出了希钦系统的Beilinson-Drinfeld量子化的二次部分，而它们的无限能级极限给出了同构方程的汉密尔顿描述。
英文摘要：
We apply the technique of localization for vertex algebras to the Segal-Sugawara construction of an ``internal'' action of the Virasoro algebra on affine Kac-Moody algebras. The result is a lifting of twisted differential operators from the moduli of curves to the moduli of curves with bundles, with arbitrary decorations and complex twistings. This construction gives a uniform approach to a collection of phenomena describing the geometry of the moduli spaces of bundles over varying curves: the KZB equations and heat kernels on non-abelian theta functions, their critical level limit giving the quadratic parts of the Beilinson-Drinfeld quantization of the Hitchin system, and their infinite level limit giving a Hamiltonian description of the isomonodromy equations.
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