Noncommutative 't Hooft Instantons
Olaf Lechtenfeld, Alexander D. Popov
Abstract
We employ the twistor approach to the construction of U(2) multi-instantons `a la 't Hooft on noncommutative R4. 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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