Title: 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 $\nu=\frac12$, 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.