Particle-vortex duality in topological insulators and superconductors

Abstract

We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of "self-duality in odd dimensions". In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son's conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.

11 pages, no figures; typos corrected, references added and updated

References in corpus (7)

• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex and Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$/ABJM correspondence
• Effective field theories for superconducting systems with multiple Fermi surfaces
• Vortex Condensation in the Dual Chern-Simons Higgs Model

Cited by in corpus (84)

• Deconfined quantum critical points: symmetries and dualities
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Dual Boundary Conditions in 3d SCFT's
• Phases Of Adjoint QCD${}_3$ And Dualities
• A Symmetry Breaking Scenario for QCD${}_3$
• Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
• Three-dimensional dualities with bosons and fermions
• An Introduction to Higher-Form Symmetries
• 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
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Embedding three-dimensional bosonization dualities into string theory
• Fermionized parafermions and symmetry-enriched Majorana modes
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
• A master bosonization duality
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Realizing topological surface states in a lower-dimensional flat band
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Dualities and Phases of 3D N=1 SQCD
• Symmetry enriched U(1) quantum spin liquids
• Bosonizing three-dimensional quiver gauge theories
• 3d Abelian Dualities with Boundaries
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• S-Dual of Maxwell Chern-Simons Theory
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• 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
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Synthetic Flux Attachment
• Parity Anomaly and Duality Web
• Double-Trace Flows and the Swampland
• Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• 3d N=4 Bootstrap and Mirror Symmetry
• Matter Chern Simons Theories in a Background Magnetic Field
• Penrose limits and spin chains in the GJV/CS-SYM duality
• Topological pumping of quantum correlations
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Charting the phase diagram of QCD${}_3$
• Quantum Hall Effect and Langlands Program
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Transport phenomena and Weyl correction in effective holographic theory of momentum dissipation
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term
• Chern-Simons dualities with multiple flavors at large $N$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• $QC{D}_3$ Dualities and the F-Theorem
• One-dimensional bosonization and the SYK model
• Particle-vortex duality and theta terms in AdS/CMT applications
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Fermion-fermion duality in 3+1 dimensions
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Phases of $\mathbf{U}({\mathbf{N}}_{\mathbf{c}})$ QCD${}_3$ from Type 0 Strings and Seiberg Duality
• Fermionic dualities with axial gauge fields
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Trialities of minimally supersymmetric 2d gauge theories
• Wiedemann-Franz laws and $Sl(2,\mathbb{Z})$ duality in AdS/CMT holographic duals and one-dimensional effective actions for them
• Chern-Simons-Matter Theories at Large Baryon Number
• Bosonization of the Thirring Model in 2+1 Dimensions
• Roton-phonon excitations in Chern-Simons matter theory at finite density
• Scaling and Diffusion of Dirac Composite Fermions
• On valley asymmetry in a topological interaction for quasi-particles
• Generalized extremal branes in AdS/CMT and holographic superconductors
• Renormalized Kalb-Ramond model: duality and generalized potential
• Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
• Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality
• A Duality Web in Condensed Matter Systems
• Domain Wall and Three Dimensional Duality
• Duality as a Method to Derive a Gauge Invariant Massive Electrodynamics and New Interactions
• Fermion-Vortex Interactions in Axion Electrodynamics