Elongated U(1) Instantons on Noncommutative R^4

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.

16 pages, 8 figures, JHEP macros, some changes in the text, some typos corrected

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• Noncommutative Solitons and D-branes
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• Space-Time Foam From Non-Commutative Instantons
• Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
• Noncommutative Instantons via Dressing and Splitting Approaches
• Comments on Noncommutative ADHM Construction
• Instanton Number Calculus on Noncommutative R^4
• Instanton Number of Noncommutative U(n) gauge theory
• Noncommutative Cohomological Field Theory and GMS soliton
• Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
• Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices
• Propagators in Noncommutative Instantons
• Noncommutative Deformation of Instantons
• Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective
• Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons