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 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 fro...

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Bibliographic Details
Published in:The journal of high energy physics 2021-08, Vol.2021 (8)
Main Authors: Gang, Dongmin, Kim, Sungjoon, Lee, Kimyeong, Shim, Myungbo, Yamazaki, Masahito
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Dictionaries
Elementary Particles
Field theory
Free energy
High energy physics
Lower bounds
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Topology
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Summary:A bstract 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 α ( − log| S 0 α + |) = max α ( − 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.
ISSN:1029-8479
DOI:10.1007/JHEP08(2021)158