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We study the mirror symmetry of abelian 3d $\mathcal{N}=2$ theories withmixed Chern-Simons levels by turning them into $\mathcal{T}_{A,N}$ theoriesthat are defined as $N$ copies of $U(1)-[1]$ theory coupled together by mixedChern-Simons levels $k_{ij}$. We find that $\mathcal{T}_{A,N}$ theories havemany mirror dual theories with different mixed CS levels and FI parameters. Asan example, we analyze $U(1)_k+ N_C \,\mathbf{C} + N_{AC} \, \mathbf{AC}$theories by transforming these theories into certain $\mathcal{T}_{A,N}$theories and find many equivalent effective Chern-Simons levels. Finally, weanalyze mirror symmetry for theories corresponding to knots. In this work weuse sphere partition functions and vortex partition functions to derive dualtheories.

Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N} = 2$ theories