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arXiv 0905.4631hep-th
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Chern-Simons理论与拓扑引力的耦合

The Coupling of Chern-Simons Theory to Topological Gravity

Camillo Imbimbo

摘要:

我们将Chern-Simons规范理论耦合到三维拓扑引力中,目的是研究它的量子拓扑不变性。我们得到了相关的BRST规则和Batalin-Vilkovisky作用。用包含反场和拓扑引力超鬼的项修正了规范场的标准BRST变换。除了与度规和引力子的明显耦合之外,BV作用量还包括迄今为止被忽视的与超鬼的耦合。我们使用这个结果来确定某些更高的鬼变形的SU(N)陈-西蒙斯理论的拓扑异常,介绍了多年前由威滕。在拓扑弦的上下文中,这些异常,概括了熟悉的框架异常,预计将被取消的耦合的封闭弦部门。我们表明,这样的耦合得到的封闭弦场的拓扑重力观测值。

英文摘要:

We couple Chern-Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin-Vilkovisky action. Standard BRST transformations of the gauge field are modified by terms involving both its anti-field and the super-ghost of topological gravity. Beyond the obvious couplings to the metric and the gravitino, the BV action includes hitherto neglected couplings to the super-ghost. We use this result to determine the topological anomalies of certain higher ghost deformations of SU(N) Chern-Simons theory, introduced years ago by Witten. In the context of topological strings these anomalies, which generalize the familiar framing anomaly, are expected to be cancelled by couplings of the closed string sector. We show that such couplings are obtained by dressing the closed string field with topological gravity observables.

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