Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d N = 2 theories
Abstract
We study the mirror symmetry of abelian 3d N=2 theories with mixed Chern-Simons levels by turning them into TA,N theories that are defined as N copies of U(1)-[1] theory coupled together by mixed Chern-Simons levels kij. We find that TA,N theories have many mirror dual theories with different mixed CS levels and FI parameters. As an example, we analyze U(1)k+ NC \,C + NAC \, AC theories by transforming these theories into certain TA,N theories and find many equivalent effective Chern-Simons 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.
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