Noncommutative 't Hooft Instantons
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0109209,
title = {Noncommutative 't Hooft Instantons},
author = {Olaf Lechtenfeld and Alexander D. Popov},
journal= {arXiv preprint arXiv:hep-th/0109209},
year = {2009}
}
Comments
1+20 pages; v2: projection clarified, gauge potential corrected, section 4 partially rewritten; v3: some formulae modified, ADHM description added