Families of Monads and Instantons from a Noncommutative ADHM Construction

We give a theta-deformed version of the ADHM construction of 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 instantons (i.e. noncommutative families of anti-self-dual connections) on the deformed sphere S_θ^4. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.