S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group

BJ Schroers, F. A. Bais

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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 languageEnglish
Pages (from-to)197-218
Number of pages22
JournalNuclear Physics B
Volume535
Issue number1-2
DOIs
Publication statusPublished - 7 Dec 1998

Keywords

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

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