Supersymmetric hybrid inflation and current-carrying metastable cosmic strings in $SU(4{)}_c\times SU(2{)}_L\times U(1{)}_R$

We construct a realistic supersymmetric model for superheavy metastable cosmic strings (CSs) that can be investigated in the current pulsar timing array (PTA) experiments. It is based on shifted $\mu$-hybrid inflation in which the symmetry breaking $SU(4{)}_c\times SU(2{)}_L\times U(1{)}_R\to SU(3{)}_c\times SU(2{)}_L\times U(1{)}_{B-L}\times U(1{)}_R$ proceeds along an inflationary trajectory such that the topologically unstable primordial monopoles are inflated away. {{The breaking of $U(1{)}_{B-L}\times U(1{)}_R\to U(1{)}_Y$ after inflation ends yields the superheavy metastable CSs carrying the right handed neutrino zero modes that generate the stochastic gravitational wave background (SGWB), which we show is consistent with the current PTA data set and the LIGO O3 run}}. The scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ are compatible with the Planck 2018 and Atacama Cosmology Telescope measurements. Both reheating and leptogenesis are briefly discussed.