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We use ideas on integrability in higher dimensions to define Lorentzinvariant field theories with an infinite number of local conserved currents.The models considered have a two dimensional target space. Requiring theexistence of Lagrangean and the stability of static solutions singles out aclass of models which have an additional conformal symmetry. That is used toexplain the existence of an ansatz leading to solutions with non trivial Hopfcharges.Comment: 30 pages, plain late

Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions