3D TFTs and boundary VOAs from BPS spectra of $(G,G^{\prime })$ Argyres-Douglas theories

Abstract

We explore 3d $\mathcal{N}=4$ theories arising from twisted compactification of 4d $\mathcal{N}=2$ $(G,G^{\prime })$ Argyres-Douglas superconformal field theories (SCFTs), together with the 2d vertex operator algebras (VOAs) supported on the holomorphic boundary of their topologically twisted sector. Starting from the Coulomb branch BPS spectra of the $(G,G^{\prime })$ Argyres-Douglas theories, we develop a systematic and efficient method to obtain the ellipsoid partition functions of associated 3d theories using quiver mutations and wall-crossing invariants. This allows us to extract the modular data of the boundary VOAs, which are related to the Schur sectors of the 4d theories through the 4d SCFT/2d VOA correspondence. Our results provide a useful computational bridge between 4d SCFTs and 2d VOAs through interpolating 3d topological field theories.

73 pages, 10 figures, v2: minor corrections