Mirror symmetry and mixed Chern-Simons levels for Abelian 3D N=2 theories

We study the mirror symmetry of Abelian three-dimensional (3D) N = 2 theories with mixed Chern-Simons (CS) levels by turning them into T-A,T-N theories that are defined as N copies of U(1)-theory coupled together by mixed CS levels k(ij). We find that T-A,T-N theories have many mirror dual theories with different mixed CS levels and Fayet-Iliopoulos parameter. As an example, we analyze U(1)(k) + NCC + N(AC)AC theories by transforming these theories into certain T-A,T-N theories and find many equivalent effective CS levels. Finally, we analyze mirror symmetry for theories corresponding to knots. In this work we use sphere partition functions and vortex partition functions to derive dual theories.

Automated summary

This study investigates the mirror symmetry of Abelian three-dimensional N = 2 theories with mixed Chern-Simons levels by transforming them into T-A,T-N theories. It reveals that T-A,T-N theories have multiple mirror dual theories with different mixed CS levels and parameters, and analyzes the mirror symmetry for theories corresponding to knots using sphere partition functions and vortex partition functions.