Tunneling gap of laterally separated quantum Hall systems

We use a method of matched asymptotics to determine the energy gap of two counter-propagating, strongly interacting quantum Hall edge states. The microscopic edge state dispersion and Coulomb interactions are used to precisely constrain the short-distance behavior of an integrable field theory, which then determines the low energy spectrum. We discuss the relationship of our results to the tunneling measurements of Kang [Nature 403, 59 (2000)].