Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/97256
Title: Monopoles, vortices, and kinks in the framework of noncommutative geometry
Authors: Teo, E. 
Ting, C. 
Issue Date: 15-Aug-1997
Citation: Teo, E.,Ting, C. (1997-08-15). Monopoles, vortices, and kinks in the framework of noncommutative geometry. Physical Review D - Particles, Fields, Gravitation and Cosmology 56 (4) : 2291-2302. ScholarBank@NUS Repository.
Abstract: 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 Z2 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.
Source Title: Physical Review D - Particles, Fields, Gravitation and Cosmology
URI: http://scholarbank.nus.edu.sg/handle/10635/97256
ISSN: 05562821
Appears in Collections:Staff Publications

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