Level/rank Duality and Chern-Simons-Matter Theories

TL;DR

This paper provides a detailed analysis of level/rank duality in 3D Chern-Simons theories, resolving puzzles, deriving dualities, and discovering new dualities including boson/boson and fermion/fermion types.

Contribution

It introduces new level/rank dualities and clarifies the role of background fields and counterterms in 3D Chern-Simons-matter dualities.

Findings

Resolved puzzles in known dualities.

Derived new dualities including boson/boson and fermion/fermion.

Established consistency conditions for dualities.

Abstract

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. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.