Real versus Complex Fermion Bare Mass and Multi-Wall String Defect Annihilation

summary

Video file (mp4)

The gist

The gist: The authors propose a novel mechanism for triggering the annihilation of cosmological domain walls in theories with global U(1) symmetries by introducing a tiny bare fermion mass term,

In short

The paper proposes a mechanism to annihilate cosmological domain walls (DWs) arising from a global U(1) symmetry breaking, which is usually cosmologically problematic. The authors show that introducing a small bare mass term for fermions coupled to the symmetry-breaking scalar generates a temperature-dependent vacuum bias through radiative corrections. This bias drives the DW collapse and complete annihilation, resolving the cosmological DW problem.

Key concepts

Domain Walls (DWs)
Topological defects formed in the early universe when a continuous global symmetry spontaneously breaks. They arise from phase transitions and can lead to cosmic strings attached to multiple walls. Their slow scaling behavior threatens the Universe's energy density.
Global U(1) Symmetry Breaking
A continuous symmetry, like electromagnetism, is broken down to a discrete subgroup by gravitational effects at the Planck scale. This breaking leads to the formation of string-wall networks where domain walls are attached to cosmic strings.
Bare Fermion Mass and Radiative Bias
Introducing a small bare mass term for fermions coupled to the symmetry-breaking scalar allows loop corrections (radiative corrections) to generate a temperature-dependent bias in the vacuum. This bias provides the necessary force to drive domain wall collapse and subsequent annihilation.
Majoron Model Example
The paper uses a majoron framework with right-handed neutrinos as an example. Gravitational operators induce a string-wall network, and the small bare masses of these right-handed neutrinos are shown to be the source of the vacuum bias that triggers DW annihilation.

Terminology used across episodes

This episode discusses

The paper

Real versus Complex Fermion Bare Mass and Multi-Wall String Defect Annihilation · Read on arXiv

Utsav Atta, *Tathagata Ghosh †Sudip Manna

Harish-Chandra Research Institute · Homi Bhabha National Institute

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.

Transcript

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Real versus Complex Fermion Bare Mass and Multi-Wall String Defect Annihilation".

Jocelyn: The gist:

Vera: First, who's behind it and why it matters.

Paper summary: Vera: To recap, this paper explores how global U(one) symmetries get broken by gravity into discrete subgroups, creating domain walls that are cosmologically troublesome <ref:2606.08142#pg1>. They propose that a small bare fermion mass term coupled to the symmetry-breaking scalar can cause radiative corrections to generate a temperature-dependent bias.

Jocelyn: That bias is what triggers the annihilation of these domain walls, and they use a majoron framework with right-handed neutrinos as their working example to show this in action.

Subrahmanyan: They've done some detailed work on how the low-energy effective potential for the majoron field looks, which resembles a standard Sine-Gordon potential after integrating out heavy fields like the radial scalar rho.

Vera: They then show how this leads to discrete vacua characterized by an integer k, and they explain that these vacua are parametrized as v over two times i to the power of two pi k over n <ref:2606.08142#pg1>.

Jocelyn: The key result they highlight is that the potential structure allows for a DW solution in the form of chi equals two pi k over n plus four v over n tan minus one e m chi x, which is a standard way to describe domain walls <ref:2606.08142#pg1>.

Subrahmanyan: And they connect this back to the bare mass term by approximating the majoron mass m chi as proportional to g over n times square root of two divided by M times n minus four times Planck length.

Vera: This connects everything together: the bare mass sets up the bias, which interacts with the structure induced by gravity and symmetry breaking to drive the annihilation.

Jocelyn: The paper also makes a point about how even-dimensional operators behave differently than odd-dimensional ones in terms of what bare mass is needed for complete annihilation.

Subrahmanyan: So, if you're looking at the bigger picture, this work provides a concrete mechanism where quantum gravitational effects leave us with a stable vacuum state instead of an infinite network of domain walls.

Conclusion: Vera: So, looking at "Real versus Complex Fermion Bare Mass and Multi-Wall String Defect Annihilation," the authors are showing that you don't need some complicated new physics beyond the standard model to solve this specific cosmological issue.

Jocelyn: It’s about demonstrating that by including a tiny bare mass term for a fermion, we can get a dynamical process—a temperature-dependent bias—that handles the annihilation of these domain walls on its own.

Subrahmanyan: The implication is that the vacuum structure induced by gravity itself isn't just some nuisance; it actively drives the system toward an annihilation state.

Vera: It’s about showing that even when you have explicit symmetry breaking from gravity, a specific type of bare mass term can lead to a stable outcome.

Jocelyn: And the authors found that this works for any number of domain walls attached to a string, which is a very strong result for topological defect physics.

Subrahmanyan: It simplifies the picture by showing that the DW problem is resolved because no stable network survives, which is what we need before Big Bang Nucleosynthesis gets too sensitive.

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