Graded unitarity in the SCFT/VOA correspondence

Journal article

Vertex algebras that arise from four-dimensional, 𝒩 = 2 superconformal field theories inherit a collection of novel structural properties from their four-dimensional ancestors. Crucially, when the parent SCFT is unitary, the corresponding vertex algebra is not unitary in the conventional sense. In this paper, we motivate and define a generalized notion of unitarity for vertex algebras that we call graded unitarity, and which captures the consequences of four-dimensional unitarity under this correspondence. We also take the first steps towards a classification program for graded-unitary vertex algebras whose underlying vertex algebras are Virasoro or affine Kac-Moody vertex algebras. Remarkably, under certain natural assumptions about the ℜ-filtration for these vertex algebras, we show that only the (2, p) central charges for Virasoro VOAs and boundary admissible levels for 𝔰𝔩2 and 𝔰𝔩3 Kac-Moody vertex algebras can possibly be compatible with graded unitarity. These are precisely the cases of these vertex algebras that are known to arise from four dimensions.

Authors: Ardehali, AA; Beem, C; Lemos, M; Rastelli, L

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2026
• Issue: 6
• Article number: 75
• Publication date: 2026-06-05
• Acceptance date: 2026-04-25
• DOI: 10.1007/jhep06(2026)075
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Conformal and W Symmetry; Extended Supersymmetry