PIRSA:17030013 Scientific Series Mathematical physics

DOI10.48660/17030013

Series: Mathematical Physics

Treumann, D. (2017). F-fields. Perimeter Institute. https://pirsa.org/17030013

Treumann, David. F-fields. Perimeter Institute, Mar. 20, 2017, https://pirsa.org/17030013 

@misc{ pirsa_PIRSA:17030013,
  doi = {10.48660/17030013},
  url = {https://pirsa.org/17030013},
  author = {Treumann, David},
  keywords = {Mathematical physics},
  language = {en},
  title = {F-fields},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {mar},
  note = {PIRSA:17030013 see, \url{https://pirsa.org}}
}

Abstract

An F-field on a manifold M is a local system of algebraically closed fields of characteristic p.  You can study local systems of vector spaces over this local system of fields.  On a 3-manifold, they are are rigid, and the rank one local systems are counted by the Alexander polynomial.  On a surface, they come in positive-dimensional moduli (perfect of characteristic p), but they are more "stable" than ordinary local systems in the GIT sense.  When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way.  On S^1 x R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it.

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