TL;DR
This paper reviews vortex solutions in gauge theories with spontaneous symmetry breaking, covering Abelian and non-Abelian cases, semilocal vortices, axion couplings, and the role of supersymmetry in BPS equations.
Contribution
It provides a comprehensive overview of vortex solutions across various gauge theories, including extensions to Yang-Mills, Chern-Simons, and supersymmetric models.
Findings
Derivation of vortex solutions in Abelian Higgs and Yang-Mills theories.
Analysis of semilocal vortices and axion couplings.
Connection between supersymmetry and BPS equations.
Abstract
I discuss in these lectures vortex-like classical solutions to the equations of motion of gauge theories with spontaneous symmetry breaking. Starting from the Nielsen-Olesen ansatz for the Abelian Higgs model, extensions to the case in which gauge dynamics is governed by Yang-Mills and Chern-Simons actions are presented. The case of semilocal vortices and also the coupling to axions is analyzed. Finally, the connection between supersymmetry and the existence of first order BPS equations in such models is described.
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Taxonomy
TopicsCosmology and Gravitation Theories · Black Holes and Theoretical Physics · Quantum chaos and dynamical systems