]>

Figure 1: The Abelian Higgs potential in the complex plane $[\Re (\mathrm{\Phi }),\Im (\mathrm{\Phi })]$. The nontrivial phase mapping from the internal space to the physical space (right) leads to the formation of a cosmic string. The old vacuum $|\mathrm{\Phi }|=0$ becomes trapped inside the new one $|\mathrm{\Phi }|={\eta }_{\text{v}}$.