Instantons on Noncommutative R4 and Projection Operators
Open Access
- 1 May 2000
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 103 (5) , 1043-1068
- https://doi.org/10.1143/ptp.103.1043
Abstract
The noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz, is carefully studied. Noncommutative R4 is described by an algebra of operators acting in a Fock space. In the ADHM construction of instantons, one looks for zero-modes of the Dirac-like operator. The feature peculiar to the noncommutative case is that these zero-modes project out some states in the Fock space. The mechanism of these projections is clarified in the case that the gauge group is U(1). In U(N) cases, it is shown in some explicit examples that projections similar to those in the U(1) cases also appear. A physical interpretation of these projections in the IIB matrix model is also discussed.Keywords
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