Chern–Simons functional under gauge transformations on flat bundles

Yanghyun Byun, Joohee Kim

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

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 Chern–Simons 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 so-called Maurer-Cartan 3-form when restricted to each fiber.

Original languageEnglish
Pages (from-to)82-93
Number of pages12
JournalJournal of Geometry and Physics
Volume111
DOIs
StatePublished - 2017 Jan 1

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Gauge Transformation
bundles
Bundle
Principal Bundle
homology
uniqueness
Cohomology
Uniqueness
Fiber
fibers
Class
Form

Keywords

  • 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

Cite this

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Chern–Simons functional under gauge transformations on flat bundles. / Byun, Yanghyun; Kim, Joohee.

In: Journal of Geometry and Physics, Vol. 111, 01.01.2017, p. 82-93.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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 Chern–Simons 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 so-called Maurer-Cartan 3-form when restricted to each fiber.

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