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Topology, and (in)stability of non-Abelian monopoles
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Zhang, Peng-Ming, Horvathy, Peter A. and Rawnsley, John H.. (2012) Topology, and (in)stability of non-Abelian monopoles. Annals of Physics, Vol.327 (No.1). pp. 118-165. ISSN 0003-4916
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Official URL: http://dx.doi.org/10.1016/j.aop.2011.09.003
Abstract
The stability problem of non-Abelian monopoles with respect to "Brandt-Neri-Coleman type" variations reduces to that of a pure gauge theory on the two-sphere. Each topological sector admits exactly one stable monopole charge, and each unstable monopole admits 2 Sigma(2 vertical bar q vertical bar - 1) negative modes, where the sum goes over the negative eigenvalues q of an operator related to the non-Abelian charge Q of Goddard, Nuyts and Olive. An explicit construction for the [up-to-conjugation] unique stable charge, as well as the negative modes of the Hessian at any other charge is given. The relation to loops in the residual group is explained. From the global point of view, the instability is associated with energy-reducing two-spheres, which, consistently with the Morse theory, generate the homology of the configuration space. Our spheres are tangent to the negative modes at the considered critical point, and may indicate possible decay routes of an unstable monopole as a cascade into lower lying critical points. (C) 2011 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Annals of Physics |
| Publisher: | Academic Press |
| ISSN: | 0003-4916 |
| Date: | 2012 |
| Volume: | Vol.327 |
| Number: | No.1 |
| Number of Pages: | 48 |
| Page Range: | pp. 118-165 |
| Identification Number: | 10.1016/j.aop.2011.09.003 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | National Natural Science Foundation of China, Chinese Academy of Sciences (CAS) |
| Grant number: | 11035006, 11175215 (NNSFC) 2010TIJ06 (CAS) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/42184 |
Data sourced from Thomson Reuters' Web of Knowledge
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