Level/rank Duality and Chern-Simons-Matter Theories

Understand

We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories.

• We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric).
• The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields.
• In order for the duality to be valid we must add finite counterterms depending on these background fields.