PIRSA:25110061 Conference Mathematical physics

DOI10.48660/25110061

Conference/School: Holomorphic-topological field theories and representation theory

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}}
}

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.

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