Abstract
Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above ${10}^{14}\text{ }\text{ }\mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow the possible range of the cosmic string scale and restricts the unified couplings and the unification scale by requiring gauge coupling unification. As an indirect consequence of the high cosmic string scale, the monopole abundance places nontrivial constraints on the theory. These are complementary to the proton decay constraints and probe different facets of supersymmetric $SO(10)$ unification theories.
Highlights
The structure of the Standard Model (SM) matter sector, quarks and leptons, and the high-energy behavior of the SM gauge couplings strongly suggest that the three SM gauge groups GSM ≡ SUð3ÞC × SUð2ÞL × Uð1ÞY are unified at a high-energy scale [1]
Supersymmetric grand unification based on SOð10Þ is one of the most attractive paradigms in physics beyond the Standard Model
Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above 1014 GeV that is favored by observable primordial gravitational waves
Summary
The structure of the Standard Model (SM) matter sector, quarks and leptons, and the high-energy behavior of the SM gauge couplings strongly suggest that the three SM gauge groups GSM ≡ SUð3ÞC × SUð2ÞL × Uð1ÞY are unified at a high-energy scale [1]. The interpretation of the NANOGrav signal with cosmic strings from a GUT phase transition indicates the existence of intermediate steps [50,51,52,53,54] in the breaking of SOð10Þ → GSM × M (with M the matter parity) because the SOð10Þ breaking predicts monopoles that may overclose the universe. It turns out that the unification of gauge couplings enforces high intermediate scales that are needed by the cosmic string interpretation of the NANOGrav result. Observation of cosmic string GW does imply the existence of an intermediate scale and strongly motivates supersymmetric SOð10Þ as the unified theory of gauge interactions.
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