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ALE spaces from noncommutative U (1) instantons via exact Seiberg-Witten map

Salizzoni, M, Torrielli, A and Yang, HS (2006) ALE spaces from noncommutative U (1) instantons via exact Seiberg-Witten map PHYSICS LETTERS B, 634 (4). 427 - 433. ISSN 0370-2693

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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.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters B, 634(4), March 2006, DOI 10.1016/j.physletb.2006.01.072.
Uncontrolled Keywords: Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, noncommutative instanton, exact Seiberg-Witten map, Eguchi-Hanson metric, FIELD-THEORIES, GAUGE-FIELDS, YANG-MILLS, GRAVITY, CONSTRUCTION, STRINGS, R-4
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 13 Jan 2012 10:52
Last Modified: 23 Sep 2013 18:57
URI: http://epubs.surrey.ac.uk/id/eprint/72378

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