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Three-Dimensional Topological Field Theories and Non-Unitary Minimal Models

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arxiv 2310.09080 v1 pith:K6O5LCFS submitted 2023-10-13 hep-th

Dongmin Gang , Heeyeon Kim , Spencer Stubbs This is my paper · ORCID
classification hep-th
keywords fieldmathcaltheoriesminimalmodelsnon-unitaryscftstfts
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We find an intriguing relation between a class of 3-dimensional non-unitary topological field theories (TFTs) and Virasoro minimal models $M(2,2r+3)$ with $r \geq 1$. The TFTs are constructed by topologically twisting $3d$ ${\mathcal N}=4$ superconformal field theories (SCFTs) of rank-0, i.e. having zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field theory descriptions of the SCFTs with manifest ${\mathcal N}=2$ supersymmetry, which we argue is enhanced to ${\mathcal N}=4$ in the infrared. From the UV description, we compute various partition functions of the TFTs and reproduce some basic properties of the minimal models, such as their characters and modular matrices. We expect more general correspondence between topologically twisted $3d$ ${\mathcal N}=4$ rank-0 SCFTs and $2d$ non-unitary rational conformal field theories.

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Cited by 4 Pith papers

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

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  4. An exceptionally simple family of Orthosymplectic 3d $\mathcal{N}=4$ rank-0 SCFTs

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