# On 2-Categories and 3d A-models

### APA

Khan, A. (2022). On 2-Categories and 3d A-models. Perimeter Institute. https://pirsa.org/22120016

### MLA

Khan, Ahsan. On 2-Categories and 3d A-models. Perimeter Institute, Dec. 09, 2022, https://pirsa.org/22120016

### BibTex

@misc{ pirsa_22120016, doi = {10.48660/22120016}, url = {https://pirsa.org/22120016}, author = {Khan, Ahsan}, keywords = {Mathematical physics}, language = {en}, title = {On 2-Categories and 3d A-models}, publisher = {Perimeter Institute}, year = {2022}, month = {dec}, note = {PIRSA:22120016 see, \url{https://pirsa.org}} }

Ahsan Khan Institute for Advanced Study (IAS)

## Abstract

The Fukaya category of a symplectic manifold is an excellent toy model for exploring the general structure of boundary conditions in two-dimensional topological field theories. In this talk I will explain an analogue for three dimensional theories. The natural playground for boundary conditions in d=3 is the 3d A-model into a hyperKahler target space. Here the fundamental BPS equation is the Fueter equation. I will explain how studying certain boundary value problems for the Fueter equation, one is lead to something resembling a higher categorical structure. I will then argue how a similar structure also seems to appear after performing a massive deformation by a hyperKahler moment map.

Zoom link: https://pitp.zoom.us/j/96574302292?pwd=dkpIVXN0UmFiRkdkenFzc2o2Nko0dz09