# Abelian 3d mirror symmetry and boundary conditions

### APA

Gammage, B. (2022). Abelian 3d mirror symmetry and boundary conditions. Perimeter Institute. https://pirsa.org/22060085

### MLA

Gammage, Benjamin. Abelian 3d mirror symmetry and boundary conditions. Perimeter Institute, Jun. 28, 2022, https://pirsa.org/22060085

### BibTex

@misc{ pirsa_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}, year = {2022}, month = {jun}, note = {PIRSA:22060085 see, \url{https://pirsa.org}} }

Harvard University

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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.