Metastable cosmic strings and gravitational waves from flavor symmetry breaking

Metastable cosmic strings (MSCSs) are among the best-fitting explanations of the 2023 pulsar timing array (PTA) signal for gravitational waves at nanohertz frequencies. We propose the novel possibility that a network of MSCSs generating this signal originates from the multistep spontaneous breaking of a gauged flavor symmetry. As a specific example, we construct a model of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:math> flavor symmetry in the context of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>5</e:mn><e:mo stretchy="false">)</e:mo></e:math> grand unification, where the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>S</i:mi><i:mi>U</i:mi><i:mo stretchy="false">(</i:mo><i:mn>2</i:mn><i:mo stretchy="false">)</i:mo></i:math> acts exclusively on the first two generations of the matter 10-plet, such that it is “right for leptons” and allows for large lepton mixing. The model explains the mass hierarchies of the Standard Model fermions, and predicts the string scale of the MSCSs in a range compatible with the 2023 PTA signal. Cosmic inflation is associated with the latter step of (two-step) family symmetry breaking, and the phase transition ending inflation generates the cosmic string network.