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

Arash Arabi Ardehali; Dongmin Gang; Neville Joshua Rajappa; Matteo Sacchi

doi:10.1007/JHEP09(2025)179

paper

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

arXiv:2411.00766 · doi:10.1007/JHEP09(2025)179

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 $N = 2$ Argyres-Douglas SCFTs using their $N = 1$ Agarwal-Maruyoshi-Song Lagrangians. From $(A_{1}, A_{2 n})$ we derive the Gang-Kim-Stubbs family of 3d $N = 2$ gauge theories with SUSY enhancement to $N = 4$ in the infrared, generalizing a recent derivation made in the special cases $n = 1, 2$ . Topological twists of these theories are known to yield $se mi s im pl e$ TQFTs supporting $r a t i o na l$ VOAs on holomorphic boundaries. From $(A_{1}, A_{2 n - 1})$ , $(A_{1}, D_{2 n + 1})$ , and $(A_{1}, D_{2 n})$ , we obtain three new infinite families of 3d $N = 2$ abelian gauge theories, all with monopole superpotentials, flowing to $N = 4$ SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields $n o n$ - $se mi s im pl e$ TQFTs related to $l o g a r i t hmi c$ VOAs such as $su (2)_{- 4/3}$ .

arXiv comment46 pages + an appendix, 2 figures

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

Abstract

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