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This theoretical physics paper proposes a solution to the cosmological domain wall problem that arises in particle physics models with global symmetries. The authors demonstrate that when gravitational effects break a global U(1) symmetry down to a discrete subgroup, the resulting network of cosmic strings connected to domain walls can self-annihilate through temperature-dependent quantum corrections generated by fermions with small bare masses. Using a majoron model with right-handed neutrinos as an example, they show that the specific mathematical properties of the fermion mass terms determine whether complete annihilation of these problematic structures occurs in the early universe.
Why it matters
This work addresses a significant theoretical obstacle in beyond-Standard-Model physics by showing how structures that would otherwise dominate the universe's energy density and conflict with observational constraints can naturally disappear. The mechanism could enable viable cosmological models that rely on global symmetries to explain phenomena like neutrino masses and dark matter.
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⚠️ Preprint – Noch nicht peer-reviewed
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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 work, we propose a mechanism for the annihilation of these DWs. If a fermion coupled to the symmetry-breaking scalar has a small bare mass, radiative corrections generate a temperature-dependent vacuum bias that drives DW collapse. As an example, we consider a majoron model with right-handed neutrinos, where gravity-induced operators produce a string-wall network. We show that a real bare Majorana mass is sufficient to induce complete DW annihilation for even-dimensional gravity-induced operators, whereas odd-dimensional operators require a complex bare Majorana mass whose phase lifts the residual vacuum degeneracy, enabling complete annihilation.
Source: Real versus Complex Fermion Bare Mass and Multi-Wall String Defect Annihilation