PIRSA:25110061

Graded Unitarity

Beem, C. (2025). Graded Unitarity. Perimeter Institute. https://pirsa.org/25110061

Beem, Christopher. Graded Unitarity. Perimeter Institute, Nov. 06, 2025, https://pirsa.org/25110061 

          @misc{ pirsa_PIRSA:25110061,
            doi = {10.48660/25110061},
            url = {https://pirsa.org/25110061},
            author = {Beem, Christopher},
            keywords = {Mathematical physics},
            language = {en},
            title = {Graded Unitarity},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110061 see, \url{https://pirsa.org}}
          }

Chris Beem University of Oxford

Talk numberPIRSA:25110061
DOI10.48660/25110061
Collection
Talk Type Conference
Subject

Abstract

Four dimensional N=2 SCFTs give rise to interesting vertex algebras via a cohomological construction (or alternatively via an equivariant deformation of their holomorphic/topological twists). When the parent four-dimensional theory is unitary, the resulting vertex algebra is equipped with a package of extra structures that we have dubbed "graded unitarity". I will describe this structure and some partial classification results that suggest that the vertex algebras admitting a graded unitary structure are quite exceptional. I will also describe some consequences of this structure for certain semi-infinite cohomological constructions that arise naturally in three and four dimensions.