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THE ADHM CONSTRUCTION OF INSTANTONS ON NONCOMMUTATIVE SPACES

We present an account of the ADHM construction of instantons on Euclidean space-time ℝ4 from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parametrized by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal–Groenewold plane and the Connes–Landi plane .