Topological Solitons and Non-perturbative Effects in Field Theory

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Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the simplest case, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non-Abelian vortex (color magnetic flux tube) in the CFL phase. On contrary to their proposal, we showed that three hadronic superfluid vortices must combine with three non-Abelian vortices with different colors with the total color magnetic fluxes canceled out, where the junction is called a colorful boojum.We discussed the effect of a strong magnetic field on neutron 3P2 superfluidity. We derived the Ginzburg-Landau equation in the path-integral formalism up to the next-to-leading order in the expansion of the magnetic field B. We determined the (T,B) phase diagram with temperature T, comprising three phases: the uniaxial nematic (UN) phase for B=0, D2-biaxial nematic (BN) and D4-BN phases in finite B and strong B such as magnetars, respectively, where D2 and D4 are dihedral groups. We presented the thermodynamic properties, such as heat capacities and spin susceptibility, and found that the spin susceptibility exhibits anisotropies in the UN, D2-BN, and D4-BN phases.