2026/07/22 by Cyril Closset, Adam Keyes, Sungjoon Kim
#hep-th
We study the twisted dimensional reduction of 4d N=2 Argyres--Douglas theories via the 3d/3d correspondence, focussing on (A1, A2n) theories realised as the class-S theory T[C] for a curve C with one irregular puncture. We argue the resulting 3d N=4 rank-0 superconformal field theory (SCFT) arises as the IR fixed point of a Dimofte--Gaiotto--Gukov (DGG) abelian Chern--Simons-matter (ACSM) theory T[M3(k)] for the lens space M3(k)=L(2n+3,2k), obtained by fibering C over the circle with twist k ∈ ℤ2n+3^×. The triangulation of M3(k), derived from the 4d BPS spectrum, determines the ACSM theory including its superpotential. T[M3(k)] flows to the expected SCFT when the monopole superpotential is near-maximal in a precise sense, while the maximal superpotential gives TA[M3(k)], which flows directly to a non-unitary TQFT, the topological A-twist of the SCFT. Geometrically, the SCFT and TQFT points are related by shifting conical singularities between edges of the triangulation, and we propose a correspondence between singular edges and SCFT points predicting when the SCFT is a unitary TQFT. The TQFTs from M3(k) can support 2d vertex operator algebras (VOAs) on their holomorphic boundary, including the Schur-sector VOA of the 4d SCFT for k=1. For n=k=1, our construction reproduces the minimal 3d N=4 SCFT of Gang and Yamazaki from L(5,2), where TA[M3(k)] is the Yang--Lee TQFT supporting M(2,5) on its boundary. We check our proposals in detail, reconstructing the modular structure of the IR TQFTs from partition functions on Seifert manifolds, and matching phases to determine VOA central charges c2d \bmod 8 from the ACSM data, including the gravitational Chern--Simons level.