Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs

A bstract The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 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> superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of ( A 1 , A 2 n ) Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $$ \mathcal{N}=1 $$ <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> supersymmetry. The result on the second sheet is 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> SUSY enhancing rank-0 theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs M (2 , 2 n + 3). Upon topological twist, they give non-unitary TQFTs controlled by the M (2 , 2 n + 3) modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 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> SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 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> SCFTs.