Non-unitary TQFTs from 3D N = 4 rank 0 SCFTs

A bstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT ± T T rank 0, to a (2+1) D interacting N N = 4 superconformal field theory (SCFT) T 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 = max α (− log| S₀^ (+) S 0 α + |) = max α (− log| S₀^ (-) S 0 α − |), where F is the round three-sphere free energy of T T rank 0 and S₀^ () S 0 α ± is the first column in the modular S-matrix of TFT ±. From the dictionary, we derive the lower bound on F, F ≥ − log (5-{510}) 5 − 5 10 ≃ 0. 642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal N 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.