English

Non-Commutative Instantons and the Seiberg-Witten Map

High Energy Physics - Theory 2009-11-07 v3

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

R2 v1 2026-07-22T15:06:50.285Z