Topological Charge of U(1) Instantons

Abstract

Non-singular instantons are shown to exist on noncommutative R^4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R^4 and the projection operators acting on the representation space of the noncommutative coordinates is reviewed. The integer number of instantons on the noncommutative R^4 can be understood as the winding number of the U(1) gauge field as well as the dimension of the projection on the representation space.

49 pages, 7 figures, based on talk given at APCTP-Yonsei Workshop on Noncommutative Field Theories

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• Dp-D(p+4) in Noncommutative Yang-Mills
• Comments on the U(2) Noncommutative Instanton
• Calculating the Prepotential by Localization on the Moduli Space of Instantons
• ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories
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• Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
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• Noncommutative Vortices and Instantons from Generalized Bose Operators
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• Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
• On the ADHM construction of noncommutative U(2) k-instanton
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• Dissolving D0-brane into D2-brane with background B-field