Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator

Abstract

Inspired by the recent developments of constructing novel Dirac liquid boundary states of the $3d$ topological insulator, we propose one possible $2d$ boundary state of the $3d$ bosonic symmetry protected topological state with $U(1{)}_e⋊Z_2^T\times U(1{)}_s$ symmetry. This boundary theory is described by a $(2+1)d$ quantum electrodynamics (QED${}_3$) with two flavors of Dirac fermions ($N_f=2$) coupled with a noncompact U(1) gauge field: $\mathcal{L}={\sum }_{j=1}^2{\bar{\psi }}_j{\gamma }_{\mu }({\partial }_{\mu }-i{a}_{\mu }){\psi }_j-i{A}_{\mu }^s\overline{{\psi }_i}{\gamma }_{\mu }{\tau }_{ij}^z{\psi }_j+\frac{i}{2\pi }{\epsilon }_{\mu \nu \rho }{a}_{\mu }{\partial }_{\nu }{A}_{\rho }^e$, where $a_{\mu }$ is the internal noncompact U(1) gauge field, $A_{\mu }^s$ and $A_{\mu }^e$ are two external gauge fields that couple to $U(1{)}_s$ and $U(1{)}_e$ global symmetries respectively. We demonstrate that this theory has a "self-dual" structure, which is a fermionic analogue of the self-duality of the noncompact CP${}^1$ theory with easy plane anisotropy. Under the self-duality, the boundary action takes exactly the same form except for an exchange between $A_{\mu }^s$ and $A_{\mu }^e$. The self-duality may still hold after we break one of the U(1) symmetries (which makes the system a bosonic topological insulator), with some subtleties that will be discussed.

5 pages

References in corpus (4)

• "Deconfined" quantum critical points
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect

Cited by in corpus (69)

• Deconfined quantum critical points: symmetries and dualities
• Level/rank Duality and Chern-Simons-Matter Theories
• Particle-Vortex Duality from 3d Bosonization
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Intrinsic and emergent anomalies at deconfined critical points
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• 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
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Dual Boundary Conditions in 3d SCFT's
• Bosonization and Mirror Symmetry
• A Symmetry Breaking Scenario for QCD${}_3$
• Nonsupersymmetric dualities from mirror symmetry
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• More Abelian Dualities in 2+1 Dimensions
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Three-dimensional dualities with bosons and fermions
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Emmy Noether looks at the deconfined quantum critical point
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Composite fermion duality for half-filled multicomponent Landau Levels
• 3d Abelian Gauge Theories at the Boundary
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Deconfined Quantum Critical Point on the Triangular Lattice
• New Developments in the Numerical Conformal Bootstrap
• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Symmetry enriched U(1) quantum spin liquids
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• The Dirac Composite Fermion of the Fractional Quantum Hall Effect
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Flavor and topological current correlators in parity-invariant three-dimensional QED
• Non-Abelian bosonization and modular transformation approach to superuniversality
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Non-Abelian Fermionization and Fractional Quantum Hall Transitions
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$
• Fermionic dualities with axial gauge fields
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Deconfined Quantum Critical Point with Non-locality
• Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Self-duality protected multi-criticality in deconfined quantum phase transitions
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Perturbative computation in a QED${}_3$-inspired conformal abelian gauge model on the lattice