Gravitational waves from non-Abelian Domain Walls
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I will discuss the properties of domain walls arising from non-Abelian discrete symmetries, which I refer to as non-Abelian domain walls. In particular, I focus on S4, a widely used group in lepton flavour mixing models. I will discuss how the spontaneous breaking of S4 leads to distinct vacua preserving either a residual Z2 or Z3 symmetry. This results in five types of domain walls, SI, SII, TI, TII, and TII, where the first two separate Z2 vacua and the latter three separate Z3 vacua. I will highlight that SI, TI, and TIII may be unstable in certain parameter regions, decaying into stable domain walls. I will also explore how these stable walls can collapse, generating gravitational radiation when explicit symmetry breaking is introduced. Finally, I will discuss how a symmetry-breaking scale around 100 TeV could explain the recent detection of nanohertz gravitational waves by PTA experiments.