NonUnitary TQFTs from 3d N=4 Rank0 SCFTs
 Date
 July 5 at 13:00  14:30, 2021 (JST)
 Speaker

 Dr. Myungbo Shim (Kyung Hee University, Republic of Korea)
 Venue
 via Zoom
 Language
 English
We propose a novel procedure of assigning a pair of nonunitary 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 nonunitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a nontrivial dictionary, we propose that F = max{ log S^{(+)}_{0\alpha} } = max{ log S^{()}_{0\alpha} }, where F is the round threesphere free energy of T_0 and S^{(\pm)}_{0\alpha} is the first column in the modular Smatrix of TFT_\pm. From the dictionary, we derive the lower bound on F, F > log(\sqrt{(5\sqrt{5})/10}) \simeq 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal N=4 SCFT proposed by GangYamazaki, whose associated topological theories are both the LeeYang TQFT. We explicitly work out the (rank 0 SCFT)/(nonunitary TQFTs) correspondence for infinitely many examples. Before going to the technical part, we provide some background materials including some peculiar features in 3d gauge theories, some supersymmetries, anyons, and some modular data of MTC in this talk.
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Reference
 D. Gang, S. Kim, K. Lee, M. Shim and M. Yamazaki