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- Title
Non-unitary TQFTs from 3D N = 4 rank 0 SCFTs.
- Authors
Gang, Dongmin; Kim, Sungjoon; Lee, Kimyeong; Shim, Myungbo; Yamazaki, Masahito
- Abstract
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 = maxα (− log| S 0 α + |) = maxα (− log| S 0 α − |), where F is the round three-sphere free energy of T rank 0 and 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 − 5 10 ≃ 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.
- Subjects
QUANTUM field theory; TOPOLOGICAL fields; PARTITION functions; CONFORMAL field theory
- Publication
Journal of High Energy Physics, 2021, Vol 2021, Issue 8, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP08(2021)158