W-algebras of the Deligne-Cvitanović Exceptional series and the minimal 3D N=4 SCFT

Preprint

We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related C₂-cofinite minimal W-algebras of the Deligne-Cvitanović (DC) series as boundary algebras. The construction is based on the minimal three-dimensional N = 4 superconformal field theory coupled to a topological field theory. For a Neumanntype boundary condition compatible with the topological A-twist, the algebra of boundary local operators realizes the minimal W-algebra W−_h∨/6(g, f_min). While this boundary condition is not deformable to the B-twist, we argue that a holomorphictopological (HT^B ) twist instead realizes the level-one affine algebras of the intermediate Lie algebras, providing a uniform three-dimensional origin for these vertex algebra structures.

Authors: Creutzig, T; Garner, N; Go, B; Kim, H

• Publication status: Published
• Peer review status: Not peer reviewed
• Preprint server: arXiv
• Publication date: 2026-03-18
• DOI: 10.48550/arXiv.2603.17394
• Language: English