### Abstract

We clarify several subtle points in the CP^{ N-1} model in 2 + 1 dimensions. It is shown that as a consequence of local gauge invariance the n_{A} particles, belonging to fundamental representation of SU(N) do not appear in the spectrum (in any number of dimensions) regardless of the nature of the interaction between them. In 2 + 1 dimensions we analyse the phase structure of the theory from the point of view of realization of the relevant symmetries: SU(N)/Z_{N} ⊗ U_{Φ}(1) ⊗ U_{E}(1). The symmetries U_{Φ}(1) and U_{E}(1) are gauge invariant analogs of the magnetic flux and electric charge symmetries in scalar QED. The charge of U_{E}(1) is not related to the global part of the local U(1) transformations (which counts the difference between the number of n and the number of n^{*} excitations). At the phase transition point the flavour SU(N) Z_{N} is broken down to U(N-1) while the mode of implementation of the U_{Φ}(1) is changed from Kosterlitz-Thouless to Wigner-Weyl. We provide a gauge invariant order parameter for the flavour symmetry breaking and identify the massless "photon" with the Kosterlitz-Thouless zero mode of U_{Φ}(1).

Original language | English |
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Pages (from-to) | 576-592 |

Number of pages | 17 |

Journal | Nuclear Physics, Section B |

Volume | 346 |

Issue number | 2-3 |

DOIs | |

State | Published - 17 Dec 1990 |

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^{N-1}model.

*Nuclear Physics, Section B*,

*346*(2-3), 576-592. https://doi.org/10.1016/0550-3213(90)90293-M