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