A New Route to the Annihilation of Multi-Wall String Topological Configurations

Abstract

Particle physics models beyond the Standard Model often contain global symmetries to address various unanswered questions. However, a common criticism of theories based on global symmetries is that such symmetries are generally expected to be explicitly violated by gravitational effects at the Planck scale. In the case of a global $U(1)$ symmetry, this explicit breaking can reduce the symmetry to a discrete subgroup of $U(1)$, leading to the formation of cosmic strings attached to multiple domain walls (DWs). These DWs are usually cosmologically problematic, since their slow scaling behavior can eventually dominate the energy density of the Universe, giving rise to the well-known cosmological DW problem, which is strongly constrained by Big Bang Nucleosynthesis. In this letter, we propose a new annihilation mechanism of such DWs in theories with the simplest continuous global symmetry, $U(1)$, in the presence of gravitational effects. The mechanism is as follows: if a fermion coupled to the symmetry-breaking scalar possesses a small bare mass term, radiative corrections can generate a temperature-dependent bias for triggering DW annihilation. As a representative example, we study a majoron framework containing right-handed neutrinos with small bare mass terms, in which a wall-string network can arise once gravitational effects are taken into account. Within this setup, we show that the small bare masses of the right-handed neutrinos provide the origin of the bias responsible for triggering the annihilation of the DW network.