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Noncommutative instantons from twisted conformal symmetries

Giovanni Landi·Walter D. van Suijlekom
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Abstract

We construct a five-parameter family of gauge-nonequivalent SU(2) instantons on a noncommutative four sphere $S_θ^4$ 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 on $S_θ^4$. They are obtained by acting with a twisted conformal symmetry on a basic instanton canonically associated with a noncommutative 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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BibTeXRIS

Giovanni Landi, Walter D. van Suijlekom. 2007-01-30. Noncommutative instantons from twisted conformal symmetries. https://doi.org/10.1007/s00220-006-0174-2

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