Extended supersymmetry in four-dimensional Euclidean space

Since the generators of the two SU(Z) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in Four-dimensional Euclidean space is considered in this paper. its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered. (C) 2000 Academic Press.