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Selfdual Gauge Field Vortices
Posted on 2010-04-01
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Author(s): Gabriella Tarantello Publisher: Birkhauser Boston Date : 2008 Pages : 335 Format : PDF OCR : Y Quality : Excellent Language : English ISBN-10 : 0817643109 Gauge Field theories (cf. , , , , , , , and ) have had a great impact in modern theoretical physics, as they keep internal symmetries and can account for important physical phenomena such as: spontaneous symmetry breaking (see e.g., [En1], [En2], and ), the quantum Hall effect (see e.g., , , , , and ), charge fractionalization, superconductivity, and supergravity (see e.g., , , , , , , and ). In these notes, we focus on specific examples of gauge field theories which admit a selfdual structure when the physical parameters satisfy a “critical” coupling condition that typically identifies a transition between different regimes. The selfdual regime is characterized by the presence of “special” soliton-type solutions corresponding to minimizers of the energy within certain constraints of “topological” nature. Such solutions, known as selfdual solutions, satisfy a set of first-order (selfdual) equations that furnish a “factorization” for the second-order gauge field equations. Furthermore, each class of “topologically equivalent” selfdual solutions form the space of moduli, whose characterization is one of the main objectives in gauge theory.
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