3d SUSY enhancement and non-semisimple TQFTs from four dimensions

Abstract

It has been recently shown that the celebrated SCFT${}_4$/VOA${}_2$ correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the $(A_1,A_n)$ and $(A_1,D_n)$ families of 4d $\mathcal{N}=2$ Argyres-Douglas SCFTs using their $\mathcal{N}=1$ Agarwal-Maruyoshi-Song Lagrangians. From $(A_1,A_{2n})$ we derive the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ gauge theories with SUSY enhancement to $\mathcal{N}=4$ in the infrared, generalizing a recent derivation made in the special cases $n=1,2$. Topological twists of these theories are known to yield $semisimple$ TQFTs supporting $rational$ VOAs on holomorphic boundaries. From $(A_1,A_{2n-1})$, $(A_1,D_{2n+1})$, and $(A_1,D_{2n})$, we obtain three new infinite families of 3d $\mathcal{N}=2$ abelian gauge theories, all with monopole superpotentials, flowing to $\mathcal{N}=4$ SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields $non$-$semisimple$ TQFTs related to $logarithmic$ VOAs such as $\widehat{\mathfrak{su}}(2{)}_{-4/3}$.

46 pages + an appendix, 2 figures

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Cited by in corpus (4)

• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Three Dimensional Topological Field Theories and Nahm Sum Formulas