Triangle Seminars
Wednesday, 12 Jun 2024
Hidden Unitarity in the SCFT/VOA Correspondence
Christopher Beem
(Oxford)
Abstract:
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.
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.
Posted by: QMW