Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories

Proton decay is a smoking gun signature of Grand Unified Theories (GUTs). Searches by Super-Kamiokande have resulted in stringent limits on the GUT symmetry breaking scale. The large-scale multipurpose neutrino experiments DUNE, Hyper-Kamiokande and JUNO will either discover proton or further push scale above $10^{16}$ GeV. Another possible observational consequence GUTs formation cosmic string network produced during to Standard Model gauge group. evolution such expanding Universe produces stochastic background gravitational waves which be tested number wave detectors over wide frequency range. We demonstrate non-trivial complementarity between observation from strings determining $SO(10)$ chains. show that observations could exclude via flipped $SU(5)\times U(1)$ standard $SU(5)$, while Pati-Salam intermediate symmetry, U(1)$, may favoured if large separation energy scales associated with indicated. note recent results NANOGrav experiment been interpreted as evidence for at $\sim 10^{14}$ This would strongly point towards existence GUTs, being prime candidate. combination already available constraints allows identify preferred routes Model.