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arXiv 0804.1772hep-th
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瞬子、费米子和陈-西蒙斯项

Instantons, Fermions and Chern-Simons Terms

Benjamin Collie, David Tong

摘要:

在五个时空维度中,瞬子是能量有限的孤立粒子。我们描述了这些对象中存在的陈-西蒙斯相互作用的动力学。对于U(N)瞬子,我们证明了在自洽双量子力学量子力学中,5d Chern-Simons项诱导出相应的Chern-Simons项。对于SU(N)瞬子,我们提供了一个描述的瞬子模空间上的测地线运动,修改的存在下的磁场。我们证明了这个磁场等于指数丛的第一个陈特征标。所有这些结果都是由一种简单的方法得出的,这种方法遵循了费米子被引入、变重和随后被积分出来时零模的命运。

英文摘要:

In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.

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。

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