2024/09/26 by Ardehali, Arash Arabi, Dedushenko, Mykola, Gang, Dongmin +1 · 2 citations
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2409.18130
The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d 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 (A1,A2n) Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest N=1 supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d 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 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 N=2 SCFTs.