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Solitons and instantons in gauged sigma models


Various prescriptions for gauging Sigma models, with or without Skyrme terms, will be examined and finite energy topologically stable solution constructed. The ensuing models, which will be defined in 2+1 and 3+1 dimensions, will be employed as toy models with which to probe the electroweak interactions qualitatively. The main method for this will be the semiclassical quantisation around the static solitons in 2 and 3 space dimensions, respectively. The analysis will be applied to the study of non-perturbative phenomena such as Baryon number non-conservation. The specific models to be considered are gauged O(d+1) models in d-dimensions featuring real fields, as well as Grassmanian models featuring complex valued fields. The gauge groups will be Abelian in 2 dimensions, and non-Abelian in dimensions greater than 2. The relation of the constrained field of the Sigma model and the unconstrained Higgs field of electroweak model is given by the relation between the constraint of the former and the Higgs self-interaction potential of the latter. In addition to the main part of the project described above, instanton solutions in an SU(2) gauged Grassmanian model in 4 Euclidean dimensions will also be applied to the same problems.

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Vasilika Vouton
71110 Iraklion

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