The structure of the Standard Model (SM) of particle physics points toward
grand unified theories (GUTs) where strong and electroweak interactions are
unified in a non-Abelian GUT group. The spontaneous breaking of the GUT
symmetry to the SM symmetry, together with cosmic inflation, generically leads
to metastable topological defects, the most prominent example being cosmic
strings. The gravitational-wave background (GWB) produced by a cosmic string
network is one of the candidates for an explanation of the GWB recently
observed by pulsar timing array (PTA) experiments. We review some properties of
the predicted GWB with emphasis on potential implications for GUT model
building. The most striking prediction is a GWB in the LIGO-Virgo-KAGRA band
that could be discovered in the near future.Comment: 15 pages, 6 figures; Rubakov conference, Yerevan. arXiv admin note:
text overlap with arXiv:2307.0469