# Categories of line operators in 3d N=4 gauge theories

### APA

Dimofte, T. (2018). Categories of line operators in 3d N=4 gauge theories. Perimeter Institute. https://pirsa.org/18100103

### MLA

Dimofte, Tudor. Categories of line operators in 3d N=4 gauge theories. Perimeter Institute, Oct. 29, 2018, https://pirsa.org/18100103

### BibTex

@misc{ pirsa_PIRSA:18100103, doi = {10.48660/18100103}, url = {https://pirsa.org/18100103}, author = {Dimofte, Tudor}, keywords = {Mathematical physics}, language = {en}, title = {Categories of line operators in 3d N=4 gauge theories}, publisher = {Perimeter Institute}, year = {2018}, month = {oct}, note = {PIRSA:18100103 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

A 3d N=4 gauge theory admits two topological twists, which we'll simply call A and B. The two twists are exchanged by 3d mirror symmetry. It is known that local operators in the A (resp. B) twist include the Coulomb-branch (resp. Higgs-branch) chiral rings. In this talk I will discuss the *line* operators preserved by the two twists, which in each case should have the structure of a braided tensor category.

Roughly speaking, one finds vortex lines in the A-twist and Wilson lines in the B-twist. I will propose a geometric identification of the corresponding categories, and explain how geometric calculations can be used to find the vector spaces of local operators at junctions of lines.

Combined with 3d mirror symmetry, this will lead to new dualities of braided tensor categories. [Joint work with N. Garner, M. Geracie, and J. Hilburn.]