Elongated U(1) Instantons on Noncommutative R^4
Tomomi Ishikawa, Shin-Ichiro Kuroki, Akifumi Sako
TL;DR
This paper presents an exact solution for elongated U(1) instantons on noncommutative R^4 for any instanton number, solving the deformed ADHM equations explicitly and verifying the solutions through numerical evaluation.
Contribution
It provides the first explicit solutions for elongated U(1) instantons on noncommutative R^4 for arbitrary instanton number, including explicit gauge connections and curvature.
Findings
Explicit solutions for elongated U(1) instantons were obtained.
The solutions satisfy the deformed ADHM equations.
Instanton charge was numerically verified.
Abstract
We found an exact solution of elongated U(1) instanton on noncommutative R^4 for general instanton number k. The deformed ADHM equation was solved with general k and the gauge connection and the curvature were given explicitly. We also checked our solutions and evaluated the instanton charge by a numerical calculation.
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