Non-perturbative Aspects of (2+1)D Supersymmetric Quantum Field Theories from Supersymmetric Partition Functions

Abstract

In this thesis, I propose two novel non-perturbative aspects of 3-dimensional supersymmetric quantum field theories by examining various supersymmetric partition functions. Firstly, I propose new 3d N = 2 Seiberg-like dualities with adjoint matters by considering monopole superpotential deformations. I provide nontrivial evidence of these new dualities by comparing the superconformal indices. In addition, I perform the F-maximization to check the relevance of the monopole deformation for some examples. Secondly, I propose a novel correspondence between a pair of non-unitary TQFTs and a 3D N = 4 rank 0 SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. I also propose a non-trivial dictionary between the round three-sphere free energy of SCFT and the modular S-matrix of the TQFT and derive the lower bound on the free energy for rank 0 SCFT. I explicitly work out the correspondence for infinitely many examples.