Collapsing domain walls with $\mathbb{Z}_2$-violating coupling to thermalized fermions and their impact on gravitational wave detections

We study the dynamics of domain walls formed through the spontaneous breaking of an approximate $\mathbb{Z}_2$ symmetry in a scalar field, focusing on their collapse under the influence of quantum and thermal corrections induced by a $\mathbb{Z}_2$-violating Yukawa coupling to Dirac fermions in the thermal bath. The thermal effects make the potential bias between the true and false vacua dependent on the temperature and may lead to notable variations in the annihilation temperature of domain walls, in addition to the shift caused by temperature-independent quantum corrections. These modifications could substantially alter the gravitational wave spectrum produced by collapsing domain walls, potentially providing observable signatures for future gravitational wave detection experiments.