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Harmonic spheres in compact Lie groups and extremals of a multivalued Novikov functional

In this paper we show that harmonic maps S 2 -> G of the two-dimensional sphere S 2 with the standard metric to a compact Lie group with a bi-invariant metric are connected in a natural way with extremals of a multivalued Novikov functional [1]. These results can be regarded as a Riemannian analogue of the description by Veselov and Takhtadzhyan [2] of principal chiral fields R 1 ' 1 —> G with a multivalued action functional, as introduced by Novikov in [1].