# Duality and Universal Transport in a Mixed-Dimension Electrodynamics

## TL;DR

This paper studies a duality in a mixed-dimensional Dirac fermion system, revealing self-duality at a specific coupling, and derives universal transport properties like constant conductivity and a semicircle law at certain conditions.

## Contribution

It demonstrates a strong-weak duality in a mixed-dimensional Dirac fermion theory and uncovers universal transport behaviors at the self-dual point and finite density.

## Key findings

- Electrical conductivity is frequency-independent.
- At filling factor 1/2, conductivities follow a semicircle law.
- Thermal Hall conductivity relates to thermal electric coefficients.

## 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.