Domain wall constraints on the doublet left-right symmetric model from pulsar timing array data

Recent evidence of a stochastic gravitational wave (GW) background found by NANOGrav and other pulsar timing array (PTA) collaborations has inspired many studies looking for possible sources. We consider the hypothesis that the GW signature is produced by domain walls (DWs) arising in the doublet left-right symmetric model (DLRSM) due to the spontaneous breaking of the discrete parity symmetry. The DW network consists of two types of DWs, namely $Z_2$ and $LR$ DWs, which have different surface tensions. We find kink solutions for both types of DWs and obtain the parametric dependence of the surface tension. Considering the GW signal from the DLRSM DW model with and without the contribution from supermassive black hole binaries, we perform a Bayesian analysis using the PTA data to estimate the posterior distribution and identify best-fit parameter ranges. The PTA data favors a parity-breaking scale of $\mathcal{O}(10^5)$\,GeV, and a biased potential $V_{\rm{bias}}\sim (\mathcal{O}(100)\,\rm{MeV})^4$. The model with only DLRSM DWs is slightly favored over the model where additional SMBHB contribution is considered.