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We found an exact solution of elongated U(1) instanton on noncom-mutative R 4 for general instanton number k. The deformed ADHM equation was solved with general k and the gauge connection and the curvature were given explicitly. We also checked our solutions and evaluated the instanton charge by a numerical calculation.

ABSTRUCT In noncommutative spaces, it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define " Instanton number " by the size of B α in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral… (More)

We show that it is possible to construct invariant field theory under the translation of noncommutative parameter θ µν. This is achieved by noncommutative cohomological field theory. As an example, noncommutative cohomological scalar field theory is constructed, and its partition function is calculated. The partition function is the Euler number of… (More)

ABSTRUCT In noncommutative spaces it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define " Instanton number " by the size of B α in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of… (More)

- Takashi Ito, Xiaoli Zhu, Shin-Ichiro Kuroki, Koji Kotani
- IEICE Transactions
- 2010

- Xiaoli Zhu, Shin-Ichiro Kuroki, +4 authors Takashi Ito
- IEICE Transactions
- 2007

We derive an effective Lagrangian for meson fields. This is done in the light-cone gauge for two-dimensional large-N c QCD by using the bilocal auxiliary field method. The auxiliary fields are bilocal on light-cone space and their Fourier transformation determines the parton momentum distribution. As the first test of our method, the 't Hooft equation is… (More)

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