Level/rank Duality and Chern-Simons-Matter Theories

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.

arXiv comment36 pages, clarifications about the fixed point with several flavors

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• Mirror Symmetry in Three Dimensional Gauge Theories
• Coupling a QFT to a TQFT and Duality
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Fermion Path Integrals And Topological Phases
• Chern-Simons Theory with Vector Fermion Matter
• 3d dualities from 4d dualities
• Seiberg Duality in Chern-Simons Theory
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Comments on 3d Seiberg-like dualities
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• D-brane Charges in Five-brane backgrounds
• Chern Simons duality with a fundamental boson and fermion
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Disorder Operators in Chern-Simons-Fermion Theories
• Mirror symmetry and the half-filled Landau level
• Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Algebraic Coset Conformal field theories
• Level-rank duality via tensor categories

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