Noncommutative Instantons and Solitons
Olaf Lechtenfeld
TL;DR
This paper presents a method for constructing noncommutative BPS configurations such as instantons, monopoles, and solitons across various dimensions using linear matrix equations, highlighting the dressing method for solitons.
Contribution
It introduces a systematic approach to generate noncommutative BPS solutions in multiple dimensions via linear matrix equations, emphasizing the dressing method for solitons.
Findings
Explicit construction of noncommutative instantons, monopoles, and solitons.
Application of the dressing method to noncommutative solitons.
Demonstration of solutions in various dimensions (D=4, 3, 2+1).
Abstract
I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 Yang-Mills-Higgs. Some emphasis is on the latter as a showcase for the dressing method.
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