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S-duality in SU(3) Yang-Mills Theory with Non-abelian Unbroken Gauge Group

B. J. 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 $\tilde H$. 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: Non-abelian 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 states 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.

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B. J. Schroers, F. A. Bais. 1998-08-24. S-duality in SU(3) Yang-Mills Theory with Non-abelian Unbroken Gauge Group. https://doi.org/10.1016/s0550-3213(98)00581-1

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