Topological defects and local gauge symmetry: clusters of strongly coupled equal-sign vortices.

We investigate the formation of topological defects in a strongly coupled system with local gauge symmetry by utilizing the AdS/CFT technique. Cooling the system into a superconductor phase, clusters of equal-sign vortices are formed due to the flux trapping mechanism. The appearance of clusters of equal-sign vortices is a typical character of flux trapping mechanism, distinct from Kibble-Zurek mechanism which only involves vortex-antivortex pair distributions resulting from global symmetry breaking. Study of spatial correlations and net fluxes of the equal-sign vortex clusters quantitatively support the positive correlations between vortices. The linear dependence between the vortex number density and the amplitude of initial magnetic field demonstrates the flux trapping mechanism as well.