We study U(1) and U(2) instanton solutions on noncommutative R^4 based on the noncommutative version of ADHM equation proposed by Nekrasov and Schwarz. It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4 correctly give integer instanton numbers for all cases we consider. We also show that the completeness relation in the ADHM construction is generally satisfied even for noncommutative spaces.
- Pub Date:
- March 2000
- High Energy Physics - Theory
- 15 pages, LaTex. v4: We now obtain the integer instanton number for our previous solutions after the correction of a numerical error, consistent with http://xxx.lanl.gov/abs/hep-th?0108007 by Chu, et al. It is also shown that the completeness relation is always satisfied, contrary to the claim by Chu, et al