Noncommutative Solitons and D-branes
arXiv:hep-th/0303256
Abstract
This thesis is designed for a comprehensive review of noncommutative (BPS) solitons with applications to D-brane dynamics including our works. We focus on noncommutative instantons and monopoles and study various aspects of the exact solutions by using Atiyah-Drinfeld-Hitchin-Manin (ADHM) and Nahm constructions. Finally we propose noncommutative extensions of integrable systems and soliton theories in lower dimensions in collaboration with Kouichi Toda, which would pioneer a new study area of integrable systems. Appendix is devoted to a brief and systematic review of formal aspects of ADHM/Nahm construction and Nahm transformation on commutative spaces. This article is also a step to a comprehensive review of ADHM/Nahm construction on both commutative and noncommutative spaces. Comments are welcome.
117 pages, 22 figures, LaTeX; This is based on my Ph.D thesis
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Cited by in corpus (26)
- D-brane Construction for Non-Abelian Walls
- Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation
- Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
- Integrable Noncommutative Sine-Gordon Model
- Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices
- Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles
- Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
- Noncommutative Monopoles and Riemann-Hilbert Problems
- On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits
- Towards Noncommutative Integrable Equations
- Seiberg-Witten Monopole Equations on Noncommutative R^4
- Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
- Noncommutative Moduli for Multi-Instantons
- Noncommutative Integrable Systems and Quasideterminants
- Noncommutative Instantons in 4k Dimensions
- Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
- Soliton Scattering in Noncommutative Spaces
- Noncommutative Deformation of Instantons
- Construction of Fuzzy Spaces and Their Applications to Matrix Models
- Noncommutative Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
- Topics in noncommutative integrable theories and holographic brane-world cosmology
- Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
- ADHM Construction of Noncommutative Instantons
- D-Branes in Noncommutative Field Theory
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