MS Seminar (Mathematics - String Theory)

Speaker: Tudor Dimofte (UC Davis)
Title: Categories of line operators in 3D N=4 theories
Date: Tue, Oct 15, 2019, 13:15 - 14:45
Place: Seminar Room A
Abstract: 3D N=4 gauge theories (with linear, polarizable matter) can be labeled by a complex reductive group G and a complex-linear representation R. Physical observables associated to this data produce interesting algebraic and geometric objects. Classic examples include the Higgs branch of vacua (which is the complex symplectic quotient T*R//G) and the Coulomb branch (which was recently given a mathematical definition by Braverman-Finkelberg-Nakajima). At one categorical level higher, physics predicts the existence of two braided monoidal categories of "line operators," roughly corresponding to sheaves on the Higgs and Coulomb branches. I will use a physical analysis to develop some aspects of these categories, and then propose mathematical definitions for them. Given time, I'll discuss categorical equivalences predicted by 3d mirror symmetry, and some applications to knot homology.
(Joint work with N. Garner, M. Geracie, J. Hilburn, and related to work of J. Hilburn and P. Yoo.)