On BRST Complexes coming from 4d N=2 SCFTsConfirmed

by Niklas Garner (University of Oxford)

Thursday Apr 10, 2025, 11:00 a.m. → 12:30 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

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.