Bosonization and Mirror Symmetry

Abstract

We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.

24 pages, 2 figures, 1 appendix

References in corpus (57)

• Topological Insulators in Three Dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Towards a derivation of holographic entanglement entropy
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Mirror Symmetry in Three Dimensional Gauge Theories
• Holographic c-theorems in arbitrary dimensions
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Fermion Path Integrals And Topological Phases
• Chern-Simons Theory with Vector Fermion Matter
• On the RG running of the entanglement entropy of a circle
• Is the Composite Fermion a Dirac Particle?
• Level/rank Duality and Chern-Simons-Matter Theories
• Notes on Superconformal Chern-Simons-Matter Theories
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
• Particle-Vortex Duality from 3d Bosonization
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Nonperturbative Tests of Three-Dimensional Dualities
• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• D-brane Charges in Five-brane backgrounds
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Dual Dirac liquid on the surface of the electron topological insulator
• Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Mott Transition in An Anyon Gas
• The half-filled Landau level: the case for Dirac composite fermions
• Supercurrents and Brane Currents in Diverse Dimensions
• Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
• Chern Simons duality with a fundamental boson and fermion
• SL(2,Z) Action on Three-Dimensional CFTs and Holography
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• A continuous transition between fractional quantum Hall and superfluid states
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Composite fermi liquids in the lowest Landau level
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus
• Disorder Operators in Chern-Simons-Fermion Theories
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Mirror symmetry and the half-filled Landau level
• Topological Insulators Avoid the Parity Anomaly
• Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Emergent particle-hole symmetry in the half-filled Landau level
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Particle-vortex symmetric liquid
• Pairing of particle-hole symmetric composite fermions in half-filled Landau level
• Pairing instabilities of Dirac composite fermions

Cited by in corpus (60)

• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Duality between $(2+1)d$ Quantum Critical Points
• Dual Boundary Conditions in 3d SCFT's
• Phases Of Adjoint QCD${}_3$ And Dualities
• A Symmetry Breaking Scenario for QCD${}_3$
• Nonsupersymmetric dualities from mirror symmetry
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
• Emergence of supersymmetric quantum electrodynamics
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• Composite fermion duality for half-filled multicomponent Landau Levels
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• Fermionized parafermions and symmetry-enriched Majorana modes
• Embedding three-dimensional bosonization dualities into string theory
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• A master bosonization duality
• Dualities and Phases of 3D N=1 SQCD
• Symmetry enriched U(1) quantum spin liquids
• Exceptional Chern-Simons-Matter Dualities
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Novel 3d bosonic dualities from bosonization and holography
• Fractons and exotic symmetries from branes
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Phases of QCD${}_3$ from Non-SUSY Seiberg Duality and Brane Dynamics
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• Metastable Vacua in Large-$N$ QCD${}_3$
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• $3d$ fermion-boson map with imaginary chemical potential
• Parity Anomaly and Duality Web
• Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases
• Self-Dual $\nu =1$ Bosonic Quantum Hall State in Mixed Dimensional QED
• The fermion-boson map for large d
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Quantum phase transition in many-flavor supersymmetric QED${}_3$
• 3d N=4 Bootstrap and Mirror Symmetry
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• Generalized Giveon-Kutasov duality
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• 3d $\mathcal{N}=2$ dualities for $SU(N_c)\times U(1)$ Chern-Simons gauge theories
• Chern-Simons dualities with multiple flavors at large $N$
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term
• Evidence for 3d bosonization from monopole operators
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Pre-ADS Superpotential from Confined Monopoles
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Trialities of minimally supersymmetric 2d gauge theories
• Flavor Broken QCD${}_3$ at Large N
• Discussion of the Duality in Three Dimensional Quantum Field Theory
• A Duality Web in Condensed Matter Systems
• SUSY Breaking in Monopole Quivers