Exceptional Chern-Simons-Matter Dualities

Abstract

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is $(E_N{)}_1\leftrightarrow SU(9-N{)}_{-1}$. Others such as $SO(3{)}_8\leftrightarrow PSU(3{)}_{-6},$ are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant $G_2$ gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

arXiv comment27 pages, 3 figures

References in corpus (39)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Generalized Global Symmetries
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Fermion Path Integrals And Topological Phases
• Chern-Simons Theory with Vector Fermion Matter
• Interacting anyons in topological quantum liquids: The golden chain
• Exploring 2-Group Global Symmetries
• Level/rank Duality and Chern-Simons-Matter Theories
• Interacting fermionic topological insulators/superconductors in three dimensions
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Particle-Vortex Duality from 3d Bosonization
• On 2-Group Global Symmetries and Their Anomalies
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Dual Dirac liquid on the surface of the electron topological insulator
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Supersymmetric Index Of Three-Dimensional Gauge Theory
• Chern Simons duality with a fundamental boson and fermion
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Phases Of Adjoint QCD${}_3$ And Dualities
• Bosonization and Mirror Symmetry
• A Symmetry Breaking Scenario for QCD${}_3$
• Three-dimensional dualities with bosons and fermions
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Anomaly indicators for time-reversal symmetric topological orders
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
• Dualities and Phases of 3D N=1 SQCD
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Holographic aspects of three dimensional QCD from string theory
• A study of time reversal symmetry of abelian anyons

Cited by in corpus (16)

• Symmetries and Strings of Adjoint QCD${}_2$
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Generalized Global Symmetries of $T[M]$ Theories. I
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Anomalies of Generalized Symmetries from Solitonic Defects
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Metastable Vacua in Large-$N$ QCD${}_3$
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Galois Conjugation and Multiboundary Entanglement Entropy
• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• 3d exceptional gauge theories and boundary confinement
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities