Instanton number calculus on noncommutative R**4
Jan, 200228 pages
Published in:
- JHEP 08 (2002) 028
e-Print:
- hep-th/0201196 [hep-th]
Report number:
- HUPD-0117
View in:
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Abstract: (arXiv)
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. Here we define ``Instanton number'' by the size of in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of Pontrjagin class (instanton charge) with the Fock space representation. Our approach is for the arbitrary converge noncommutative U(1) instanton solution, and is based on the anti-self-dual (ASD) equation itself. We give the Stokes' theorem for the number operator representation. The Stokes' theorem on the noncommutative space shows that instanton charge is given by some boundary sum. Using the ASD conditions, we conclude that the instanton charge is equivalent to the instanton number.Note:
- 29 pages, 7 figures, some statements in Sec.4.3 corrected
- space-time: noncommutative
- instanton: charge
- Stokes theorem
- gauge field theory: U(N)
- symmetry: U(1)
- Fock space
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