### Abstract

The noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz, is carefully studied. Noncommutative R^{4} 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.

Original language | English |
---|---|

Pages (from-to) | 1043-1068 |

Number of pages | 26 |

Journal | Progress of Theoretical Physics |

Volume | 103 |

Issue number | 5 |

DOIs | |

Publication status | Published - 01-01-2000 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

}

^{4}and projection operators',

*Progress of Theoretical Physics*, vol. 103, no. 5, pp. 1043-1068. https://doi.org/10.1143/PTP.103.1043

**Instantons on noncommutative R ^{4} and projection operators.** / Furuuchi, Kazuyuki.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Instantons on noncommutative R4 and projection operators

AU - Furuuchi, Kazuyuki

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034336834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034336834&partnerID=8YFLogxK

U2 - 10.1143/PTP.103.1043

DO - 10.1143/PTP.103.1043

M3 - Article

VL - 103

SP - 1043

EP - 1068

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -

^{4}and projection operators. Progress of Theoretical Physics. 2000 Jan 1;103(5):1043-1068. https://doi.org/10.1143/PTP.103.1043