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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/270694 |
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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 |