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Self duality solution with a Higgs field

The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO(3) Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.