### Abstract

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in Ref. [J. Polchinski, L. Thorlacius, Phys. Rev. D 50 (1994) 622]. We find that the entire SL (2, C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strong-weak coupling generalization of T-duality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the self-dual radius. These have simple expression in fermion variables. We postulate sine-Gordon-like field theories with discrete gauge symmetries for which they are the appropriate boundary states.

Original language | English (US) |
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Pages (from-to) | 2849-2875 |

Number of pages | 27 |

Journal | Annals of Physics |

Volume | 321 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2006 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*321*(12), 2849-2875. https://doi.org/10.1016/j.aop.2006.02.006