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

A bstract 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 $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> Argyres-Douglas SCFTs using their $$ \mathcal{N}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> Agarwal-Maruyoshi-Song Lagrangians. From ( A 1 , A 2 n ) we derive the Gang-Kim-Stubbs family of 3d $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> gauge theories with SUSY enhancement to $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> 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 2 n −1 ), ( A 1 , D 2 n +1 ), and ( A 1 , D 2 n ), we obtain three new infinite families of 3d $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> abelian gauge theories, all with monopole superpotentials, flowing to $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> 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 $$ \hat{su}{(2)}_{-4/3} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>su</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:msub> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> .