Non-Commutative Instantons and the Seiberg-Witten Map
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.
Keywords
Cite
@article{arxiv.hep-th/0110035,
title = {Non-Commutative Instantons and the Seiberg-Witten Map},
author = {Per Kraus and Masaki Shigemori},
journal= {arXiv preprint arXiv:hep-th/0110035},
year = {2009}
}
Comments
26 pages, AMS-LaTeX. v2: the formula for the commutative description of the Nekrasov-Schwarz instanton corrected (sec. 4). v3: minor corrections