The ADHM construction of instantons on noncommutative spaces

摘要

We present an account of the ADHM construction of instantons on Euclidean space-time ?~4 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 MoyalGroenewold plane ?~4h and the ConnesLandi plane ?~4_θ.