PIRSA ID: 23120034

Series:

Event Type: Seminar

Scientific Area(s): Mathematical Physics

End date: 2023-12-07

Speaker(s): Tudor Dimofte Tudor Dimofte University of Edinburgh

December 7, 2023 at 11:00 AM

Space Room

I will discuss an explicit way to construct Hopf algebras and quasi-triangular Hopf algebras (their Drinfeld doubles) within 3d TQFT, using extended operators on boundary conditions -- dubbed `spark' algebras. The representation categories of these algebras capture boundary and bulk line operators. Overall, the construction realizes Tannakian duality geometrically; in perturbative TQFT's, it is closely connected to the holographic Koszul duality of Costello and Paquette. I'll illustrate the construction for Dijkgraaf-Witten theory (a.k.a. gauge theory with finite gauge group), and then sketch an application to the B-type topological twist of 3d N=4 gauge theories, which initially motivated these investigations. (Work in progress with T. Creutzig and W. Niu.)

---

Zoom link https://pitp.zoom.us/j/93746215441?pwd=YjdhaDNFeko3VDVKQW5ZV1MzL1cvUT09