2011/05/20 by Antonella D'Avanzo, D'Avanzo, Antonella
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Chromodynamics and Particle Interactions #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1105.4153
PhD thesis - 137 pages, 23 figures
arxiv created 2011/05/20 · arxiv updated 2011/05/23
Monopoles are solutions of an SU(2) gauge theory in ℝ3 satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable systems, monopoles can be described in algebraic-geometric terms via their spectral curve, i.e. an algebraic curve, given as a polynomial P in two complex variables, satisfying certain constraints. In this thesis we focus on the Ercolani-Sinha formulation, where the coefficients of P have to satisfy the Ercolani-Sinha constraints, given as relations amongst periods. A particular class of such monopoles is studied, namely charge 3 monopoles with a symmetry by C3, the cyclic group of order 3. This class of cyclic 3-monopoles is described by the genus 4 spectral curve X, subject to the Ercolani-Sinha constraints: the aim of the present work is to establish the existence of such monopoles, which translates into solving the Ercolani-Sinha constraints for X.