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

TL;DR

This work develops a systematic framework to extract 3d physics from 4d Argyres-Douglas theories via a $U(1)_r$-twisted circle reduction using their $ N=1$ UV Lagrangians. By applying Cardy-limit index techniques to the Agarwal-Maruyoshi-Song Lagrangians, it identifies four infinite families of 3d $ N=2$ theories that exhibit IR SUSY enhancement to $ N=4$ SCFTs or flow to TQFTs, with detailed CS data, monopole superpotentials, and Higgs/Coulomb-branch structure matching the 4d parents. The paper provides explicit constructions for the Gang-Kim-Stubbs family from $(A_1,A_{2n})$ and three new abelian families from $(A_1,A_{2n-1})$, $(A_1,D_{2n+1})$, and $(A_1,D_{2n})$, including in-depth analyses of the $(A_1,A_3)$, $(A_1,A_5)$, $(A_1,D_3)$, $(A_1,D_5)$ cases and their Higgs-branch Hilbert series. It further studies A-twisted TQFT modular data, matching the simplest case to the admissible $igl( ext{SU}(2)_{-4/3}igr)$ VOA, and explores conjugate theories on the opposite sheet, providing a bridge between non-semisimple and unitary TQFTs through shared partition functions.

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 $\widehat{\mathfrak{su}}(2)_{-4/3}$.

Figures (2)

• Figure 1: The plot of $12Q^{\gamma=1}(x)$ versus $x$ for $(A_1,A_3)$. The interior region between $x=\pm1/6$ is flat and the value of $Q^{\gamma=1}$ there is zero.
• Figure 2: The plot of $L^{\gamma=1}_{R_0}(x)$ versus $x$ for $(A_1,A_3)$. The minima at $x=\pm1/6$ are exactly zero. The interior slopes are $2.$