PIRSA:17050033

Vacua and Singular Supports

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}}
          }

Chris Elliott University of Massachusetts Amherst

DOI 10.48660/17050033
Collection
Talk Type Scientific Series
Subject

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.