PIRSA:25040114

On BRST Complexes coming from 4d N=2 SCFTs

Garner, N. (2025). On BRST Complexes coming from 4d N=2 SCFTs. Perimeter Institute. https://pirsa.org/25040114

Garner, Niklas. On BRST Complexes coming from 4d N=2 SCFTs. Perimeter Institute, Apr. 10, 2025, https://pirsa.org/25040114 

          @misc{ pirsa_PIRSA:25040114,
            doi = {10.48660/25040114},
            url = {https://pirsa.org/25040114},
            author = {Garner, Niklas},
            keywords = {Mathematical physics},
            language = {en},
            title = {On BRST Complexes coming from 4d N=2 SCFTs},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {apr},
            note = {PIRSA:25040114 see, \url{https://pirsa.org}}
          }

Niklas Garner University of Washington

Talk numberPIRSA:25040114
DOI10.48660/25040114
Collection
Talk Type Scientific Series
Subject

Abstract

Vertex operator algebras (VOAs) arise in many corners of supersymmetric quantum field theory. One particularly influential instance is in 4d N=2 superconformal field theories, whereby the VOA is realized as the cohomology of a suitable supercharge. Unitarity of the underlying SCFT imposes strong constraints on the structure of the resulting VOA. In this talk, I will describe one aspect of how the unitary of the underlying SCFT constrains this VOA: in the context of superconformal gauge theories, the resulting BRST complex shares a striking resemblance to the de Rham complex of a compact Kähler manifolds. I will finish with several consequences of this observation, e.g. the formality of these BRST complexes as in the work of Deligne-Griffiths-Morgan-Sullivan on compact Kähler manifold. This is based on work in progress with C. Beem.