Families of Monads and Instantons from a Noncommutative ADHM Construction
arXiv:0901.0772
Abstract
We give a θ-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families' of SU(2) instantons on the deformed sphere S^4_θ. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.
v2: 29 pages, minor changes. Final version to appear in a special volume of the Clay Mathematics Institute dedicated to Alain Connes