Cosmic Strings in Multi-Step Symmetry Breaking

We investigate cosmic strings arising from a hierarchical gauge symmetry breaking sequence, $\mathrm{SU}(2) \times \mathrm{U}(1) \rightarrow \mathrm{U}(1) \times \mathrm{U}(1) \rightarrow \mathrm{U}(1)' \rightarrow \text{Nothing}$. This pattern gives rise to two distinct classes of cosmic strings: light, stable strings formed at a later stage, and heavy, metastable strings originating from an earlier stage. Our focus is on the heavy strings, which may decay either before or after the final $\mathrm{U}(1)'$ symmetry is broken. We analyze the internal structure of these strings and the magnetic flux sourced by monopole-like configurations that emerge at the endpoints of metastable string segments following their decay. Understanding the nature of the magnetic $\mathrm{U}(1)$ fluxes associated with these monopole-like objects is crucial for studying the post-decay evolution of the string network. The post-decay evolution influences the resulting gravitational wave signals. We show that the magnetic flux carried by string segments can be either confined or unconfined, depending on the specific sequence of symmetry breaking and string decay.