ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories

Abstract

We study the relationship between ADHM/Nahm construction and ``solution generating technique'' of BPS solitons in noncommutative gauge theories. ADHM/Nahm construction and ``solution generating technique'' are the most strong ways to construct exact BPS solitons. Localized solitons are the solitons which are generated by the ``solution generating technique.'' The shift operators which play crucial roles in ``solution generating technique'' naturally appear in ADHM/Nahm construction and we can construct various exact localized solitons including new solitons: localized periodic instantons (=localized calorons) and localized doubly-periodic instantons. Nahm construction also gives rise to BPS fluxons straightforwardly from the appropriate input Nahm data which is expected from the D-brane picture of BPS fluxons. We also show that the Fourier-transformed soliton of the localized caloron in the zero-period limit exactly coincides with the BPS fluxon.

30 pages, LaTeX, 3 figures; v3: minor changes, references added; v4: references added, version to appear in PRD

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• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Noncommutative Instantons via Dressing and Splitting Approaches
• Non-Commutative Instantons and the Information Metric
• Spherically symmetric monopoles in noncommutative space
• New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model
• Instanton Number of Noncommutative U(n) gauge theory
• Band spectrum is D-brane
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
• Lost equivalence of nonlinear sigma and $C{P}^1$ models on noncommutative space
• Construction of Noncommutative Instantons in 4k Dimensions
• Propagators in Noncommutative Instantons
• Instantons on General Noncommutative R^4
• General classical solutions in the noncommutative CP^(N-1) model
• Noncommutative Instantons on CP^n
• On Non-Commutative Orbifolds of K3 Surfaces
• BPS Solutions of Noncommutative Gauge Theories in Four and Eight Dimensions
• Unstable solitons on noncommutative tori and D-branes
• Matrix model for noncommutative gravity and gravitational instantons
• ADHM Construction of Noncommutative Instantons
• On the ADHM construction of noncommutative U(2) k-instanton
• Gauge theory solitons on noncommutative cylinder
• Noncommutative instantons on $d=2n$ planes from matrix models