We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
3D mirror symmetry and the βγ VOA.
- Authors
Ballin, Andrew; Niu, Wenjun
- Abstract
We study the simplest example of mirror symmetry for 3d = 4 SUSY gauge theories: the A-twist of a free hypermultiplet and the B-twist of SQED. We particularly focus on the category of line operators in each theory. Using the work of Costello–Gaiotto, we define these categories as appropriate categories of modules for the boundary vertex operator algebras present in each theory. For the A-twist of a free hyper, this will be a certain category of modules for the β γ VOA, properly containing the category previously studied by Allen-Wood. Applying the work of Creutzig–Kanade–McRae and Creutzig–McRae–Yang, we show that the category of line operators on the A side possesses the structure of a braided tensor category, extending the result of Allen-Wood. In addition, we prove that there is a braided tensor equivalence between the categories of line operators on the A side and B side, completing a nontrivial check of the 3d mirror symmetry conjecture. We derive explicit fusion rules as a consequence of this equivalence and obtain interesting relations with associated quantum group representations.
- Subjects
VOICE of America (Organization); MIRROR symmetry; GAUGE field theory; BRAIDED structures; QUANTUM groups; OPERATOR theory; VERTEX operator algebras
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 1, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199722500699