Selfdual Gauge Field Vortices: An Analytical Approach

Gabriella Tarantello (auth.)9780817643102, 0817643109, 0817646086

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of gauge field theories that exhibit a selfdual structure.

The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of the subject and formulating examples ranging from the well-known abelian–Higgs and Yang–Mills models to the Chern–Simons–Higgs theories (in both the abelian and non-abelian settings). Thereafter, the electroweak theory and self-gravitating electroweak strings are also examined, followed by the study of the differential problems that have emerged from the analysis of selfdual vortex configurations; in this regard the author treats elliptic problems involving exponential non-linearities, also in relation to concentration-compactness principles and blow-up analysis.

Many open questions still remain in the field and are examined in this comprehensive work in connection with Liouville-type equations and systems. The goal of this text is to form an understanding of selfdual solutions arising in a variety of physical contexts. Selfdual Gauge Field Vortices: An Analytical Approach is ideal for graduate students and researchers interested in partial differential equations and mathematical physics.

Table of contents :
Front Matter….Pages i-xiv
Selfdual Gauge Field Theories….Pages 1-41
Elliptic Problems in the Study of Selfdual Vortex Configurations….Pages 43-74
Planar Selfdual Chern–Simons Vortices….Pages 75-130
Periodic Selfdual Chern–Simons Vortices….Pages 131-172
The Analysis of Liouville-Type Equations With Singular Sources….Pages 173-248
Mean Field Equations of Liouville-Type….Pages 249-279
Selfdual Electroweak Vortices and Strings….Pages 281-303
Back Matter….Pages 305-325