Abstract: 3d N=4 gauge theories admit two distinct topological twists, ‘A’ and ‘B’, analogous to the well-studied A and B twists of 2d N=(2,2) theories, and exchanged by 3d mirror symmetry. Unlike their 2d analogues, much of the categorical structure of the 3d twists is still being worked out. I will discuss some aspects of the category of line operators in the A and B of gauge theories, and an application to knot homology, deriving the A-twisted mirror of a construction of Oblomkov-Rozansky.
Joint work with Niklas Garner, Justin Hilburn, Alexei Oblomkov, and Lev Rozansky.