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.

Families of Monads and Instantons from a Noncommutative ADHM Construction

LANDI, GIOVANNI
2010-01-01

Abstract

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.
2010
9780821852033
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1898126
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