Non-Commutative Instantons and the Seiberg-Witten Map
arXiv:hep-th/0110035 · doi:10.1088/1126-6708/2002/06/034
Abstract
We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These include the two dimensional ``shift operator'' solutions and the four dimensional Nekrasov-Schwarz instantons as special cases. We also study how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal Seiberg-Witten map is shown to take a very simple form in operator language, and this result is used to give a commutative description of non-commutative instantons. The instanton is found to be singular in commutative variables.
26 pages, AMS-LaTeX. v2: the formula for the commutative description of the Nekrasov-Schwarz instanton corrected (sec. 4). v3: minor corrections
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