We construct a five-parameter family of gauge nonequivalent SU(2) instantons on a noncommutative four sphere and of topological charge equal to 1. These instantons are critical points of a gauge functional and satisfy self-duality equations with respect to a Hodge star operator on forms. They are obtained by acting with a twisted conformal symmetry on a basic instanton canonically associated with a non- commutative instanton bundle on the sphere. A completeness argument for this family is obtained by means of index theorems. The dimension of the “tangent space” to the moduli space is computed as the index of a twisted Dirac operator and turns out to be equal to five, a number that survives deformation.

Noncommutative instantons from twisted conformal symmetries

LANDI, GIOVANNI;
2007

Abstract

We construct a five-parameter family of gauge nonequivalent SU(2) instantons on a noncommutative four sphere and of topological charge equal to 1. These instantons are critical points of a gauge functional and satisfy self-duality equations with respect to a Hodge star operator on forms. They are obtained by acting with a twisted conformal symmetry on a basic instanton canonically associated with a non- commutative instanton bundle on the sphere. A completeness argument for this family is obtained by means of index theorems. The dimension of the “tangent space” to the moduli space is computed as the index of a twisted Dirac operator and turns out to be equal to five, a number that survives deformation.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/1695868
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