Zero-Field Hall Effect in (2+1)-dimensional QED

In three-dimensional QED, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid-state physics, the Hall conductivity for rational magnetic flux is expected to be given by a Chern number. In our field-free situation, however, the conductivity is ±1/2 in natural units. We explain why the integrality of the conductivity breaks down and explain its quantisation geometrically. For quasi-periodic boundary conditions, we calculate the finite size correction to the Hall conductivity. Our paper establishes an explicit connection between quantum fied theory and solid-state physics.