Four-dimensional N=2 superconformal field theories give rise, via a cohomological construction that I will review, to associated vertex operator algebras that have been much investigated in the last decade. A curiosity of this construction is that for unitary parent SCFT, the vertex operator algebras so-realised are non-unitary. In this talk I will present the structure on these VOAs that encodes unitarity of the parent theory. Like conventional unitarity, this hidden unitarity imposes strong constraints. I will describe efforts to impose this constraint for Virasoro VOAs (and possibly affine Kac–Moody vertex algebras) leading to (conjectural) classification results for central charges/levels at which these algebras are compatible with four-dimensional unitarity. The talk is based on work in progress with A. Ardehali, M. Lemos, and L. Rastelli.

I will review the recently exposed connection between N=2 superconformal field theories in four dimensions and vertex operator algebras (VOAs). I will outline some general features of the VOAs that arise in this manner and describe the manner in which they reflect four-dimensional operations such as gauging and Higgsing. Time permitting, I will also touch on the modular properties of characters of these VOAs.