arXiv 1009.22452010-09math.AGmath-phmath.MP

从WZW模型到模函子

From WZW models to Modular Functors

Eduard Looijenga

备注：: In this revision (2) we give a somewhat clearer exposition of projectively flat connections (Sect. 1) and of the passage to a topological interpretation of the story (Sect. 7). Otherwise the modifications are minor. It will appear in the Handbook of Moduli

摘要：

在这篇综述论文（它取代了我们早期的arXiv预印本math.AG/0507086）中，我们给出了WZW模型作为一个局部系统的一个相对简单和无坐标的描述，它的基是一个在尖曲线的模栈上的G_m丛。我们推导出它的主要性质，并显示它如何导致一个模块化函子的精神格雷姆西格尔（除了么正性）。这里提出的方法几乎是纯粹的代数几何性质，它避免了玻色子费米子对应，操作乘积展开式以及Teichmueller理论。

英文摘要：

In this survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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