Superheavy Metastable Strings in SO(10)

The spontaneous breaking of $SO(10)$ grand unified symmetry to $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)_\chi$ yields the GUT monopole as well as a comparably heavy $U(1)_\chi$ monopole which also carries $U(1)_Y$ flux. A metastable string scenario in this case requires that the $U(1)_\chi$ symmetry is necessarily broken close to the GUT scale, thus resulting in a dimensionless string tension $G \mu \sim 10^{-6}$. We show that the $\chi$ monopole does not carry any unconfined flux following the electroweak symmetry breaking. Coupled with $G \mu \sim 10^{-6}$, this metastable string network appears to provide a good fit to the recent Pulsar Timing Array data on the stochastic gravitational background. Gauge coupling unification, especially in the presence of low scale supersymmetry, determines the GUT scale and, in combination with constraints from proton decay experiments, one is able to constrain some of the key parameters in this setup. The breaking of $SO(10)$ via $SU(5) \times U(1)_\chi$ also yields superheavy metastable strings with no unconfined flux associated with the monopoles. Finally, we consider $SO(10)$ breaking via $SU(4)_c \times SU(2)_L \times U(1)_R$, $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ and flipped $SU(5)$ that yield metastable strings where the associated monopoles carry unconfined flux after the electroweak breaking.