Universal Transverse Conductance between Quantum Hall Regions and (2+1)D Bosonization

Using bosonization techniques for (2+1)D systems, we show that the transverse conductance for a system with general current interactions, when measured between perfect Hall regions is not renormalized at low temperatures. Our method extends and combines two results we have recently obtained on low dimensional fermionic systems: on the one hand, the relationship between universality of Landauer conductance and universality of bosonization rules for (1+1)D systems, and on the other hand, the universal character of the bosonized topological current associated to a (2+1)D fermionic system with current interaction.