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Noncommutative deformation of instantons and vortexes. (English) Zbl 1171.81410

Summary: We study noncommutative (NC) instantons and vortexes. At first, we construct instanton solutions which are deformations of instanton solutions on commutative Euclidean four-space. We show that the instanton numbers of these NC instanton solutions coincide with the commutative solutions. Next, we also deform vortex solutions similarly and we show that their vortex numbers are unchanged under the NC deformation.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81R60 Noncommutative geometry in quantum theory
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