56 research outputs found
On Exact Noncommutative BPS Solitons
We construct new exact BPS solitons in various noncommutative gauge theories
by the ``gauge'' transformation of known BPS solitons. This ``gauge''
transformation introduced by Harvey, Kraus and Larsen adds localized solitons
to the known soliton. These solitons include, for example, the bound state of a
noncommutative Abelian monopole and N fluxons at threshold. This corresponds,
in superstring theories, to a D-string which attaches to a D3-brane and N
D-strings which pierce the D3-brane, where all D-strings are parallel to each
other.Comment: 18 pages, LaTeX, 2 figures; v3: minor changes, comments added,
references added; v4: version to appear in JHE
ADHM Construction of Noncommutative Instantons
We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N)
instantons in noncommutative (NC) space and prove the one-to-one correspondence
between moduli spaces of the noncommutative instantons and the ADHM data,
together with an origin of the instanton number for U(1). We also give a
derivation of the ADHM construction from the viewpoint of the Nahm
transformation of instantons on four-tori. This article is a composite version
of [23] and [24].Comment: 23pages, 3 figures, LaTeX; A composite version of proceedings of the
20th International Colloquium on Integrable Systems and Quantum Symmetries
(ISQS20), 17-23 June 2012, Prague, Czech Republic and the 10th International
Conference on Symmetries and Integrability of Difference Equations (SIDE10),
11-15 June 2012, Ningbo, Chin
Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations
We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard
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