Self-Dual $\nu=1$ Bosonic Quantum Hall State in Mixed Dimensional QED

Understand

We consider a (2+1) dimensional Wilson-Fisher boson coupled to a (3+1) dimensional U(1) gauge field.

• This theory possesses a strong-weak duality in terms of the coupling constant e, and is self-dual at a particular value of $e$.
• We derive exact relations between transport coefficients for a $\nu=1$ quantum Hall state at the self-dual point.
• Using boson-fermion duality, we map the $\nu=1$ bosonic quantum Hall state to a Fermi sea of the dual fermion, and observed that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random phase approximation, coupled with a Drude formula, in the fermionic theory.