Noncommutative Instantons from Twisted Conformal Symmetries |
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Authors: | Giovanni Landi Walter D van Suijlekom |
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Institution: | (1) Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy;(2) INFN, Sezione di Trieste, Trieste, Italy;(3) Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany |
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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 on . 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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Keywords: | |
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