  The edge state theory of a class of symmetric double-layer quantum Hall
systems with interlayer electron tunneling reduces to the sum of a free field
theory and a field theory of a chiral Bose field with a self-interaction of the
sine-Gordon form. We argue that the perturbative renormalization group flow of
this chiral sine-Gordon theory is distinct from the standard (non-chiral)
sine-Gordon theory, contrary to a previous assertion by Renn, and that the
theory is manifestly sensible only at a discrete set of values of the inverse
period of the cosine interaction (beta). We obtain exact solutions for the
spectra and correlation functions of the chiral sine-Gordon theory at the two
values of beta at which the electron tunneling in bilayers is not irrelevant.
Of these, the marginal case (beta^2=4) is of greatest interest: the spectrum of
the interacting theory is that of two Majorana fermions with different,
dynamically generated, velocities. For the experimentally observed bilayer 331
state at filling factor 1/2, this implies the trifurcation of electrons added
to the edge. We also present a method for fermionizing the theory at the
discrete points (integer beta^2) by the introduction of auxiliary degrees of
freedom that could prove useful in other problems involving quantum Hall
multilayers.
