Families of Monads and Instantons from a Noncommutative ADHM Construction

Details Families of Monads and Instantons from a Noncommutative ADHM Construction Families of Monads and Instantons from a Noncommutative ADHM Construction

2009-01-07

arxiv.org/abs/0901.0772v2

Clay Math.Proc.11: 55-84,2010

Mathematics

Quantum Algebra

v2: 29 pages, minor changes. Final version to appear in a special volume of the Clay Mathematics Institute dedicated to Alain

Scientific paper

We give a \theta-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_\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.

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