paper

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

arXiv:hep-th/9805163 · doi:10.1016/S0550-3213(98)00581-1

Abstract

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group are in one-to-one correspondence with coherent states of a dual or magnetic group . 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.

27 pages, harvmac, amssym, one eps figure; minor misprints corrected and title amended

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