  In this work, we investigate the relation between higher-dimensional gauge
theories and stochastic gravitational wave (GW) spectrums caused by their
potential. It is known that the higher-dimensional gauge theories can induce
the spontaneous symmetry breaking of the gauge symmetry. If the spontaneous
symmetry breaking induces the first-order phase transition, the stochastic GW
can be observed in future interferometers. Through our numerical calculations,
we reveal that distinctive parameters in the theories, like the compact scale,
can change the GW spectrums dynamically. We also discuss the verifiability of
the theories through the GW observations.
