Duality and Universal Transport in a Mixed-Dimension Electrodynamics

Abstract

We consider a theory of a two-component Dirac fermion localized on a (2+1) dimensional brane coupled to a (3+1) dimensional bulk. Using the fermionic particle-vortex duality, we show that the theory has a strong-weak duality that maps the coupling $e$ to $\tilde{e}=(8\pi )/e$. We explore the theory at $e^2=8\pi$ where it is self-dual. The electrical conductivity of the theory is a constant independent of frequency. When the system is at finite density and magnetic field at filling factor $\nu =\frac{1}{2}$, the longitudinal and Hall conductivity satisfies a semicircle law, and the ratio of the longitudinal and Hall thermal electric coefficients is completely determined by the Hall angle. The thermal Hall conductivity is directly related to the thermal electric coefficients.

arXiv comment6 pages

References in corpus (23)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Is the Composite Fermion a Dirac Particle?
• Quantum critical transport, duality, and M-theory
• Particle-Vortex Duality from 3d Bosonization
• 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
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• More Abelian Dualities in 2+1 Dimensions
• Universal relation between longitudinal and transverse conductivities in quantum Hall effect
• Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• Duality and bosonization of (2+1)d Majorana fermions
• Topological Insulators Avoid the Parity Anomaly
• Self Duality and a possible Hall-insulator phase near the superconductor-to-insulator transition in two-dimensional indium-oxide films
• Critical behaviour of reduced QED${}_{4,3}$ and dynamical fermion gap generation in graphene
• Holographic DC conductivity and Onsager relations
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• The method of uniqueness and the optical conductivity of graphene: new application of a powerful technique for multi-loop calculations
• Line of continuous phase transitions in a three dimensional U(1) model with 1/r^2 current-current interactions

Cited by in corpus (29)

• Boundary Conformal Field Theory and a Boundary Central Charge
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• An Analytic Approach to BCFT${}_d$
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• 3d Abelian Gauge Theories at the Boundary
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• On Marginal Operators in Boundary Conformal Field Theory
• Conformal Surface Defects in Maxwell Theory are Trivial
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Superconformal Models for Graphene and Boundary Central Charges
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Quantum Dirac fermions in half space and their interaction with electromagnetic field
• Higher-form Symmetries under Weak Measurement
• Self-Dual $\nu =1$ Bosonic Quantum Hall State in Mixed Dimensional QED
• Screening and Topological Order in Thin Superconducting Films
• Thermoelectric Transport Coefficients from Charged Solv and Nil Black Holes
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Duality Constraints on Thermal Spectra of 3d Conformal Field Theories and 4d Quasinormal Modes
• Spontaneous symmetry breaking in free theories with boundary potentials
• Quantization of a Self-dual Conformal Theory in (2+1) Dimensions
• Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity
• Supersymmetric Graphene on Squashed Hemisphere
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities
• Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction
• Quantum critical scaling of altermagnetism
• Geometrisation of Ohm's reciprocity relation in a holographic plasma
• Critical properties of three-dimensional many-flavour QEDs
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Gauge field fluctuation corrected QED3 effective action by fermionic particle-vortex duality