  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 et al., Nature 403, 59
(2000).
