Monopoles, vortices, and kinks in the framework of noncommutative geometry
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW (England)
- Department of Computational Science, National University of Singapore, (Singapore) 119260
Noncommutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum state, should it be nonunique. A consequence is that Yang-Mills-Higgs theory can be reformulated as a generalized Yang-Mills gauge theory on Euclidean space with a {bold Z}{sub 2} internal structure. By extending the Hodge star operation to this noncommutative space, we are able to define the notion of self-duality of the gauge curvature form in arbitrary dimensions. It turns out that BPS monopoles, critically coupled vortices, and kinks are all self-dual solutions in their respective dimensions. We then prove, within this unified formalism, that static soliton solutions to the Yang-Mills-Higgs system exist only in one, two, and three spatial dimensions. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 538667
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 4 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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