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

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT +/-[T-rank 0], to a (2+1)D interacting N = 4 superconformal field theory (SCFT) 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 alpha (-log vertical bar S-0 alpha((+)) vertical bar) = max(alpha) (-log vertical bar S-0 alpha((-))vertical bar), where F is the round three-sphere free energy of T-rank 0 and S-0 alpha((+/-)) is the first column in the modular S-matrix of TFT +/-. From the dictionary, we derive the lower bound on F, F >= - log (root 5-root 5/10) similar or equal to 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. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

Automated summary

A novel procedure is proposed to assign a pair of non-unitary topological quantum field theories to a specific category of superconformal field theories. The modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in particular degenerate limits, leading to a lower bound on the round three-sphere free energy of T-rank 0. The bound is saturated by a minimal N=4 SCFT proposed by Gang-Yamazaki, with associated topological theories being the Lee-Yang TQFT.