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arXiv · hep-th/9912047

Instantons on Noncommutative R^4 and Projection Operators

Kazuyuki Furuuchi
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Abstract

I carefully study noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz. Noncommutative ${\bf R}^4$ is described as algebra of operators acting in Fock space. In ADHM construction of instantons, one looks for zero-modes of Dirac-like operator. The feature peculiar to noncommutative case is that these zero-modes project out some states in Fock space. The mechanism of these projections is clarified when the gauge group is U(1). I also construct some zero-modes when the gauge group is U(N) and demonstrate that the projections also occur, and the mechanism is similar to the U(1) case. A physical interpretation of the projections in IIB matrix model is briefly discussed.

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Kazuyuki Furuuchi. 2000-02-10. Instantons on Noncommutative R^4 and Projection Operators. https://doi.org/10.1143/ptp.103.1043

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