PIRSA:17020034

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_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}}
          }
          

Andrew Neitzke University of Texas - Austin

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.