## Abstract

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra module its Coxeter number, can be carried out irrespective of the coefficient of the Wess-Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension. (C) 2000 Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 605-646 |

Number of pages | 42 |

Journal | Nuclear Physics B |

Volume | 580 |

Issue number | 3 |

DOIs | |

Publication status | Published - 7 Aug 2000 |

## Keywords

- WESS-ZUMINO TERM
- 2 DIMENSIONS
- INVARIANT TENSORS
- FIELD-THEORIES
- SIGMA-MODELS
- INTEGRABILITY
- LAWS
- SYMMETRIES
- SCATTERING
- SYSTEMS