PIRSA:17020034 Conference Mathematical physics

DOI10.48660/17020034

Conference/School: Hitchin Systems in Mathematics and Physics

Neitzke, A. (2017). Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle. Perimeter Institute. https://pirsa.org/17020034

Neitzke, Andrew. Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle. Perimeter Institute, Feb. 17, 2017, https://pirsa.org/17020034 

@misc{ pirsa_PIRSA:17020034,
  doi = {10.48660/17020034},
  url = {https://pirsa.org/17020034},
  author = {Neitzke, Andrew},
  keywords = {Mathematical physics},
  language = {en},
  title = {Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {feb},
  note = {PIRSA:17020034 see, \url{https://pirsa.org}}
}

Abstract

I will describe an approach to classical complex Chern-Simons theory via "abelianization", relating flat SL(N)-connections over a manifold of dimension d <= 3 to flat GL(1)-connections over a branched N-fold cover. This is joint work with Dan Freed. When applied in dimension d=2 this construction leads to an alternative description of a hyperholomorphic line bundle over the moduli space of Higgs bundles, studied e.g. by Haydys, Hitchin, Alexandrov-Persson-Pioline.

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