Non-Abelian domain walls and gravitational waves

We investigate the properties of domain walls arising from non-Abelian discrete symmetries, which we refer to as non-Abelian domain walls. We focus on S₄, one of the most commonly used groups in lepton flavour mixing models. The spontaneous breaking of S₄ leads to distinct vacua preserving a residual Z₂ or Z₃ symmetry. Five types of domain walls are found, labelled as SI, SII, TI, TII, and TIII, respectively, the former two separating Z₂ vacua and the latter three separating Z₃ vacua. We highlight that SI, TI and TIII may be unstable for some regions of the parameter space and decay to stable domain walls. Stable domain walls can collapse and release gravitational radiation for a suitable size of explicit symmetry breaking. A symmetry-breaking scale of order 100 TeV may explain the recent discovery of nanohertz gravitational waves by PTA experiments. For the first time, we investigate the properties of these domain walls, which we obtain numerically with semi-analytical formulas applied to compute the tension and thickness across a wide range of parameter space. We estimate the resulting gravitational wave spectrum and find that, thanks to their rich vacuum structure, non-Abelian domain walls manifest in a very interesting and complex phenomenology.