Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle
APA
Neitzke, A. (2017). Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle. Perimeter Institute. https://pirsa.org/17020034
MLA
Neitzke, Andrew. Abelianization in complex Chern-Simons theory and a hyperholomorphic line bundle. Perimeter Institute, Feb. 17, 2017, https://pirsa.org/17020034
BibTex
@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}} }
The University of Texas at Austin
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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.