Degeneracy between Abelian and non-Abelian strings

In a model that supports both Abelian (Abrikosov-Nielsen-Olesen) and non-Abelian strings we analyze the parameter space to find examples in which these strings not only coexist but are degenerate in tension. We prove that both solutions are locally stable, i.e. there are no negative modes in the string background. The tension degeneracy is achieved at the classical level and is expected to be lifted by quantum corrections. The setup of the model, analogous to that of Witten's superconducting cosmic strings, had been extended to include non-Abelian strings previously [M. Shifman, Phys. Rev. D 87, 025025 (2013), arXiv:1212.4823 [hep-th]].