Notes on Noncommutative Instantons

Details Notes on Noncommutative Instantons Notes on Noncommutative Instantons

2001-08-01

arxiv.org/abs/hep-th/0108007v3

Nucl.Phys. B621 (2002) 101-130

Physics

High Energy Physics

High Energy Physics - Theory

Regular instanton solutions are now explicitly constructed also for the case of space-space noncommutativity

Scientific paper

10.1016/S0550-3213(01)00576-4

We study in detail the ADHM construction of U(N) instantons on noncommutative Euclidean space-time R_{NC}^4 and noncommutative space R_{NC}^2 x R^2. We point out that the completeness condition in the ADHM construction could be invalidated in certain circumstances. When this happens, regular instanton configuration may not exist even if the ADHM constraints are satisfied. Some of the existing solutions in the literature indeed violate the completeness condition and hence are not correct. We present alternative solutions for these cases. In particular, we show for the first time how to construct explicitly regular U(N) instanton solutions on R_{NC}^4 and on R_{NC}^2 x R^2. We also give a simple general argument based on the Corrigan's identity that the topological charge of noncommutative regular instantons is always an integer.

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