Recent Developments in Instantons in Noncommutative ℝ4
We review recent developments in noncommutative deformations of instantons in ℝ4. In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instanto...
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| Published in | Advances in mathematical physics Vol. 2010; no. 2010; pp. 1 - 28 |
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| Main Author | |
| Format | Journal Article |
| Language | English Japanese |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2010
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| Online Access | Get full text |
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| Summary: | We review recent developments in noncommutative deformations of instantons in ℝ4. In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instantons whose commutative limits are singular. We review smooth noncommutative deformations of instantons, spinor zero-modes, the Green's functions, and the ADHM constructions from commutative ones that have no singularities. It is found that the instanton charges of these noncommutative instanton solutions coincide with the instanton charges of commutative instantons before noncommutative deformation. These smooth deformations are the latest developments in noncommutative gauge theories, and we can extend the procedure to other types of solitons. As an example, vortex deformations are studied. |
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| ISSN: | 1687-9120 1687-9139 |
| DOI: | 10.1155/2010/270694 |