Abstract: Vertex operator algebras (VOAs) arise in many corners of supersymmetric quantum field theory. One particularly influential instance is in four-dimensional N=2 superconformal field theories (SCFTs), 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 VOAs; ongoing work of Ardehali, Beem, Lemos, and Rastelli proposes that four-dimensional unitarity is realized in the VOA via a notion they call graded unitarity.

In this talk, I will review this notion and describe structural aspects of the chain complexes underlying relative semi-infinite cohomology (alias: BRST complexes) of graded unitary VOAs. We will see that these BRST complexes share a striking resemblance to the de Rham complexes of compact Kähler manifolds. I will finish with several consequences of this observation, e.g. the formality of these relative semi-infinite cohomologies as in the work of Deligne, Griffiths, Morgan, and Sullivan on the de Rham cohomology of compact Kähler manifolds. This is based on work in progress with C. Beem.

Abstract: TBA

Abstract - TBA