Implications of gravitational waves for supersymmetric grand unification

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 1014 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