Chern-Simons functional under gauge transformations on flat bundles

被引:2
|
作者
Byun, Yanghyun [1 ]
Kim, Joohee [1 ]
机构
[1] Hanyang Univ, Dept Math, Coll Nat Sci, Wangsimni Ro 222, Seoul 133791, South Korea
关键词
Chern-Simons functional defined by a reference connection; Degree of a gauge transformation; Global Maurer-Cartan 3-form on the adjoint bundle of a flat bundle;
D O I
10.1016/j.geomphys.2016.09.012
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We describe the effect of a gauge transformation on the Chern-Simons functional in a thorough and unifying manner. We use the assumptions that the structure group is compact and connected and, in particular, that the principal bundle is flat. The ChernSimons functional we consider is the one defined by choosing a flat reference connection. The most critical step in arriving at the main result is to show both the existence and the uniqueness of a cohomology class on the adjoint bundle such that it is the class of the socalled Maurer-Cartan 3-form when restricted to each fiber. (C) 2016 Elsevier B.V. All rights reserved.
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页码:82 / 93
页数:12
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