Sigma models with N = 8 supersymmetries in 2 + 1 and 1 + 1 dimensions

We introduce an N = 8 supersymmetric extension of the Bogomolny-type model for Yang-Mills-Higgs fields in 2 + 1 dimensions related with twistor string theory. It is shown that this model is equivalent to an N = 8 supersymmetric U (n) chiral model in 2 + 1 dimensions with a Wess-Zumino-Witten-type term. Further reduction to 1 + 1 dimensions yields N = (8 , 8) supersymmetric extensions of the standard U (n) chiral model and Grassmannian sigma models.