Noncommutative Instantons via Dressing and Splitting Approaches

Details Noncommutative Instantons via Dressing and Splitting Approaches Noncommutative Instantons via Dressing and Splitting Approaches

2002-11-06

arxiv.org/abs/hep-th/0211041v4

JHEP 0212 (2002) 060

Physics

High Energy Physics

High Energy Physics - Theory

1+16 pages; v2: typos corrected, published version; v3: eq.(4.16) corrected; v4: eqs. (3.22),(3.24),(3.30),(3.31) corrected

Scientific paper

10.1088/1126-6708/2002/12/060

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.

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