Noncommutative 't Hooft Instantons

Details Noncommutative 't Hooft Instantons Noncommutative 't Hooft Instantons

2001-09-27

arxiv.org/abs/hep-th/0109209v3

JHEP 0203 (2002) 040

Physics

High Energy Physics

High Energy Physics - Theory

1+20 pages; v2: projection clarified, gauge potential corrected, section 4 partially rewritten; v3: some formulae modified, AD

Scientific paper

10.1088/1126-6708/2002/03/040

We employ the twistor approach to the construction of U(2) multi-instantons `a la 't Hooft on noncommutative R^4. The noncommutative deformation of the Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However, naively substituting into it the 't Hooft-type solution is unsatisfactory because the resulting gauge field fails to be self-dual on a finite-dimensional subspace of the Fock space. We repair this deficiency by a suitable Murray-von Neumann transformation after a specific projection of the gauge potential. The proper noncommutative 't Hooft multi-instanton field strength is given explicitly, in a singular as well as in a regular gauge.

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