On July 5, Myungo Shim from Kyung Hee University, Korea, gave the iTHEMS-physics seminar on a correspondence between three-dimensional gauge theories. He proposed a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [T_0]$, to a (2+1)D interacting $N=4$ superconformal field theory (SCFT) $T_0$ 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, he proposed that $F = {\rm max}\{ - \log |S^{(+)}_{0\alpha}| \} = {\rm max}\{- \log |S^{(-)}_{0\alpha}|\}$, where $F$ is the round three-sphere free energy of $T_0$ and $S^{(\pm)}_{0\alpha}$ is the first column in the modular S-matrix of TFT$_\pm$. From the dictionary, he derived the lower bound on $F$, $F \geq -\log \left(\sqrt{\frac{5-\sqrt{5}}{10}} \right) \simeq 0.642965$, which holds for any rank $0$ SCFT. The bound is saturated by the minimal $N=4$ SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. Before going to the technical part, he also provided some background materials including some peculiar features in 3d gauge theories, some supersymmetries, anyons, and some modular data of MTC in the talk.

Reported by Toshihiro Ota