PIRSA:17050033 Scientific Series Mathematical physics

DOI10.48660/17050033

Series: Mathematical Physics

Elliott, C. (2017). Vacua and Singular Supports. Perimeter Institute. https://pirsa.org/17050033

Elliott, Chris. Vacua and Singular Supports. Perimeter Institute, May. 15, 2017, https://pirsa.org/17050033 

@misc{ pirsa_PIRSA:17050033,
  doi = {10.48660/17050033},
  url = {https://pirsa.org/17050033},
  author = {Elliott, Chris},
  keywords = {Mathematical physics},
  language = {en},
  title = {Vacua and Singular Supports},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {may},
  note = {PIRSA:17050033 see, \url{https://pirsa.org}}
}

Abstract

The notion of singular support for coherent sheaves was introduced by Arinkin and Gaitsgory in order to carefully state the geometric Langlands conjecture.  This is a conjectural equivalence of categories of sheaves on certain moduli spaces: in order to make the conjecture reasonable one needs to restrict to sheaves which satisfy a certain "singular support condition".  In this talk I'll explain how to think about this singular support condition from the point of view of boundary conditions in twisted N=4 gauge theory.  Specifically, Arinkin and Gaitsgory's singular support condition arises by considering only those boundary conditions which are compatible with a natural choice of vacuum state.  By allowing this vacuum state to move away from this natural choice we see aspects of a rich additional structure for the geometric Langlands correspondence.  This work is joint with Philsang Yoo.

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