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

TL;DR

This paper explores the high-temperature limits of 4d $ ext{N}=2$ superconformal theories, revealing connections to 3d topological quantum field theories and 2d vertex operator algebras, with implications for SUSY enhancement and modular tensor categories.

Contribution

It introduces a novel approach linking 4d SCFTs, 3d EFTs, and 2d VOAs through high-temperature limits on higher sheets, expanding the understanding of 4d/2d correspondences.

Findings

Identifies 3d $ ext{N}=2$ theories with boundary VOAs $M(2,2n+3)$.

Shows high-temperature limits produce non-unitary TQFTs with MTCs.

Provides a systematic method for 3d SUSY enhancement from 4d SUSY enhancement.

Abstract

The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $\mathcal{N}=2$ 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 $(A_1,A_{2n})$ Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $\mathcal{N}=1$ supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ SUSY enhancing rank-$0$ theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs $M(2,2n+3)$. Upon topological twist, they give non-unitary TQFTs controlled by the $M(2,2n+3)$ 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 $\mathcal{N}=2$ 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 $\mathcal{N}=2$ SCFTs.