PIRSA:24120029

Video URL

https://pirsa.org/24120029

Vortex lines and dg-shifted Yangians

Dimofte, T. (2024). Vortex lines and dg-shifted Yangians. Perimeter Institute for Theoretical Physics. https://pirsa.org/24120029

Dimofte, Tudor. Vortex lines and dg-shifted Yangians. Perimeter Institute for Theoretical Physics, Dec. 05, 2024, https://pirsa.org/24120029 

          @misc{ scivideos_PIRSA:24120029,
            doi = {10.48660/24120029},
            url = {https://pirsa.org/24120029},
            author = {Dimofte, Tudor},
            keywords = {Mathematical physics},
            language = {en},
            title = {Vortex lines and dg-shifted Yangians},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {dec},
            note = {PIRSA:24120029 see, \url{https://scivideos.org/pirsa/24120029}}
          }

Tudor Dimofte University of Edinburgh

Talk numberPIRSA:24120029
DOI10.48660/24120029
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

I'll discuss the representation theory of line operators in 3d holomorphic-topological theories, following recent work with Wenjun Niu and Victor Py. Examples of the line operators we have in mind include half-BPS lines in 3d N=2 supersymmetric theories (reinterpreted in a holomorphic twist). We compute the OPE of line operators, which endows the category with a meromorphic tensor product, and establish a perturbative nonrenormalization theorem for the OPE. Then, applying Koszul-duality methods of Costello and Costello-Paquette, we represent the category of lines as modules for a new sort of mathematical object, which we call a dg-shifted Yangian. This is an A-infinity algebra, with a chiral coproduct whose data includes a Maurer-Cartan element that behaves like an infinitesimal r-matrix. The structure is a cohomologically shifted version of the ordinary Yangians that represent lines in 4d holomorphic-topological theories.