Surface integrals in lower dimensions from higher-order Chern classes and a class of solutions in three dimensions
- 1 January 1986
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (1) , 325-339
- https://doi.org/10.1063/1.527405
Abstract
It is shown that surface integrals, involving gauge and Higgs fields, in both odd and even dimensions can be obtained by dimensional reduction from Chern classes in higher dimensions. For odd dimensions, the physically useful dimensional reduction is characterized by ℳN=EN−p×Sp, and for even dimensions by ℳN =EN−p×S2×⋅ ⋅ ⋅×S2 ( 1/2 p times). The existence of a family of field configurations for which these surface integrals in three dimensions exist, and are nonzero, is presented. This family includes a Yang–Mills–Higgs (YMH) system with an algebra-valued Higgs field and one with the Higgs field in the reducible representation adjoint ⊕ scalar.Keywords
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