# F-fields

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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.