Abelian 3d mirror symmetry and boundary conditions

          @misc{ scivideos_PIRSA:22060085,
            doi = {10.48660/22060085},
            url = {https://pirsa.org/22060085},
            author = {Gammage, Benjamin},
            keywords = {Mathematical physics},
            language = {en},
            title = {Abelian 3d mirror symmetry and boundary conditions},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060085 see, \url{https://scivideos.org/pirsa/22060085}}
          }
          

Abstract

3d mirror symmetry predicts an equivalence between A- and B-twists of a pair of dual 3d N=4 theories. Essentially the strongest invariants one can produce of the resulting 3-dimensional topological field theories are their 2-categories of boundary conditions. The B-side 2-category was first described by Kapustin-Rozansky-Saulinas, but the 2-categorical structure on A-side boundary conditions has not previously been understood. For abelian gauge theories with matter, we propose a model for the 2-category of A-type boundary conditions using Kapranov-Schechtman's "perverse schobers," and we prove a 3d mirror equivalence between dual 2-categories. By reducing to lower-dimensions, we can recover both the BFN construction and the BLPW Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.