Abstract
We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[\( \mathcal{T} \)rank 0], to a (2+1)D interacting \( \mathcal{N} \) = 4 superconformal field theory (SCFT) \( \mathcal{T} \)rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|\( {S}_{0\alpha}^{\left(+\right)} \)|) = maxα (− log|\( {S}_{0\alpha}^{\left(-\right)} \)|), where F is the round three-sphere free energy of \( \mathcal{T} \)rank 0 and \( {S}_{0\alpha}^{\left(\pm \right)} \) is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log \( \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) \) ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal \( \mathcal{N} \) = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.
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Gang, D., Kim, S., Lee, K. et al. Non-unitary TQFTs from 3D \( \mathcal{N} \) = 4 rank 0 SCFTs. J. High Energ. Phys. 2021, 158 (2021). https://doi.org/10.1007/JHEP08(2021)158
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DOI: https://doi.org/10.1007/JHEP08(2021)158