ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
Abstract
The exact Seiberg-Witten (SW) map of a noncommutative (NC) gauge theory gives the commutative equivalent as an ordinary gauge theory coupled to a field dependent effective metric. We study instanton solutions of this commutative equivalent whose self-duality equation turns out to be the exact SW map of NC instantons. We derive general differential equations governing U(1) instantons and we explicitly get an exact solution corresponding to the single NC instanton. Remarkably the effective metric induced by the single U(1) instanton is related to the Eguchi-Hanson metric - the simplest gravitational instanton. Surprisingly the instanton number is not quantized but depends on an integration constant. Our result confirms the expected non-perturbative breakdown of the SW map. However, the breakdown of the map arises in a consistent way: The instanton number plays the role of a parameter giving rise to a one-parameter family of Eguchi-Hanson metrics.
Keywords
Cite
@article{arxiv.hep-th/0510249,
title = {ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map},
author = {Mario Salizzoni and Alessandro Torrielli and Hyun Seok Yang},
journal= {arXiv preprint arXiv:hep-th/0510249},
year = {2010}
}
Comments
15 pages, Latex; Comment on commutative limit is added and a small mistake in section 4 is corrected