### Abstract

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group (H) over tilde. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Nonabelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent slates obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.

Original language | English |
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Pages (from-to) | 197-218 |

Number of pages | 22 |

Journal | Nuclear Physics B |

Volume | 535 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 7 Dec 1998 |

### Keywords

- charge sectors in Yang-Mills theory
- non-abelian S-duality
- MAGNETIC MONOPOLES
- CHARGE
- STATES
- DYONS
- SPACE

## Cite this

*Nuclear Physics B*,

*535*(1-2), 197-218. https://doi.org/10.1016/S0550-3213(98)00581-1