Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence

[2607.20308] Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Theory arXiv:2607.20308 (hep-th) [Submitted on 22 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence Authors: Cyril Closset , Adam Keyes , Sungjoon Kim View a PDF of the paper titled Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence, by Cyril Closset and 2 other authors View PDF HTML (experimental) Abstract: We study the twisted dimensional reduction of 4d $\mathcal{N}=2$ Argyres--Douglas theories via the 3d/3d correspondence, focussing on $(A_1, A_{2n})$ theories realised as the class-$\mathcal{S}$ theory $T[\mathcal{C}]$ for a curve $\mathcal{C}$ with one irregular puncture. We argue the resulting 3d $\mathcal{N}=4$ rank-0 superconformal field theory (SCFT) arises as the IR fixed point of a Dimofte--Gaiotto--Gukov (DGG) abelian Chern--Simons-matter (ACSM) theory $T[M_3^{(k)}]$ for the lens space $M_3^{(k)}=L(2n+3,2k)$, obtained by fibering $\mathcal{C}$ over the circle with twist $k \in \mathbb{Z}_{2n+3}^\times$. The triangulation of $M_3^{(k)}$, derived from the 4d BPS spectrum, determines the ACSM theory including its superpotential. $T[M_3^{(k)}]$ flows to the expected SCFT when the monopole superpotential is near-maximal in a precise sense, while the maximal superpotential gives $T_A[M_3^{(k)}]$, 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 $M_3^{(k)}$ 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 $\mathcal{N}=4$ SCFT of Gang and Yamazaki from $L(5,2)$, where $T_A[M_3^{(k)}]$ 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 $c_{\text{2d}} \bmod 8$ from the ACSM data, including the gravitational Chern--Simons level. Comments: 71 pages, 14 figures; added several references Subjects: High Energy Physics - Theory (hep-th) Cite as: arXiv:2607.20308 [hep-th] (or arXiv:2607.20308v2 [hep-th] for this version) https://doi.org/10.48550/arXiv.2607.20308 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sungjoon Kim [ view email ] [v1] Wed, 22 Jul 2026 15:55:29 UTC (90 KB) [v2] Sat, 15 Aug 2026 05:17:23 UTC (90 KB) Full-text links: Access Paper: View a PDF of the paper titled Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence, by Cyril Closset and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-07 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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