### Abstract

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 (β̂). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β̂ at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (β̂^{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 (β̂^{2} ∋ e ℤ+) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers.

Original language | English (US) |
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Pages (from-to) | 572-610 |

Number of pages | 39 |

Journal | Nuclear Physics B |

Volume | 565 |

Issue number | 3 |

DOIs | |

State | Published - Jan 24 2000 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*565*(3), 572-610. https://doi.org/10.1016/S0550-3213(99)00658-6