From exotic superconductivity to QCD and back again searching things in common

Sammanfattning: This thesis is devoted largely to two new features which Particle Physics and Condensed Matter theory have in common. The first part of the thesis is a discussion of formation of phases precursory to the chiral phase transition in relativistic models with four-fermion interactions, considered as toy models for QCD. This discussion is based on analogy with the novel pseudogap concept in strong-coupling and low carrier density superconductors. In the second part we discuss a condensed mater realizations of knotted solitions, which were discussed earlier by Faddeev and Niemi. We argue that these defects can exist in superconducting liquid metallic hydrogen and deuterium and two-band superconductors. The knotted solitions is a novel for condensed matter concept and thus it is of great academic interest in this field. The macroscopic quantum origin of topological defects in superfluids implies its rather direct observability. This possibility to actually observe these objects, their properties, stability and interactions may result in a 'feedback" for understanding its role in the infrared limit of Yang-Mills theory complementing ongoing numerical simulations. In the third part of the thesis we study the effect of Coulumb interaction on formation of charged vortices in the Abelian Higgs model in the presence of a uniform compensating background field. This study is also of interdisciplinary interest. The description of granular superconductors and Josephson junction arrays usually includes Coulomb terms which accounts for the presence of the cristal lattice. Also it may be relevant for extreme strong coupling or low carrier density superconductors which may have vortices which r-ores are not filled by decomposed Cooper pairs. This study also allows to estimate characteristic length scales of a charged vortices which should be of interests for the studies of knotted solitons formed by two complex scalar fields with Coulomb interaction discussed by Faddeev and Niemi.