Domain Walls in $A_4$ Flavour Models

Bowen Fu; Jessica Turner; Luca Marsili; Stephen F. King; Ye-Ling Zhou

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Domain Walls in $A_4$ Flavour Models

Bowen Fu, Stephen F. King, Luca Marsili, Jessica Turner, Ye-Ling Zhou

High Energy Physics - Phenomenology · Submitted 15 Dec 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Through a detailed analysis of these models with non-Abelian symmetries, we discover new kinds of domain walls, which we denote as ``oreo''-type composite domain walls, CP-violating domain walls and SUSY non-Abelian domain walls.

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The spontaneous breaking of an $A_4$ flavour symmetry, often used to predict leptonic mixing, can lead to the formation of domain walls which can annihilate and generate a stochastic gravitational wave background. We study this phenomenon in three scenarios where the nature of the scalar field responsible for breaking the $A_4$ symmetry spontaneously differs: real, complex, and supersymmetric. For the real scalar, a biased potential produces metastable walls that decay into oscillating two-wall systems with important consequences for gravitational wave signals. In the complex scalar case, we discuss the interplay between domain walls and global strings and classify the types of domain walls that form in terms of the $A_4$ group symmetries. We investigate the properties of supersymmetric $A_4$ domain walls, and highlight the BPS walls. Through a detailed analysis of these models with non-Abelian symmetries, we discover new kinds of domain walls, which we denote as ``oreo''-type composite domain walls, CP-violating domain walls and SUSY non-Abelian domain walls. Finally we show how these results may be achieved in leptonic $A_4$ flavour models, with and without supersymmetry, and discuss their distinctive gravitational wave signatures.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The spontaneous breaking of an $A_4$ flavour symmetry, often used to predict leptonic mixing, can lead to the formation of domain walls which can annihilate and generate a stochastic gravitational wave background.	background 1.00	0.07	0.24	hedged possibility 0.81
s1	We study this phenomenon in three scenarios where the nature of the scalar field responsible for breaking the $A_4$ symmetry spontaneously differs: real, complex, and supersymmetric.	contribution 0.92	0.80	0.05	asserted 0.92
s2	For the real scalar, a biased potential produces metastable walls that decay into oscillating two-wall systems with important consequences for gravitational wave signals.	result 0.93	0.73	0.09	asserted 0.99
s3	In the complex scalar case, we discuss the interplay between domain walls and global strings and classify the types of domain walls that form in terms of the $A_4$ group symmetries.	contribution 0.92	0.89	0.06	asserted 0.95
s4	We investigate the properties of supersymmetric $A_4$ domain walls, and highlight the BPS walls.	contribution 0.97	0.88	0.06	asserted 0.97
s5	Through a detailed analysis of these models with non-Abelian symmetries, we discover new kinds of domain walls, which we denote as ``oreo''-type composite domain walls, CP-violating domain walls and SUSY non-Abelian domain walls.	result 0.81	0.95	0.50	asserted 1.00
s6	Finally we show how these results may be achieved in leptonic $A_4$ flavour models, with and without supersymmetry, and discuss their distinctive gravitational wave signatures.	result 0.37	0.90	0.37	hedged possibility 0.65

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

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Original abstract

The spontaneous breaking of an $A_4$ flavour symmetry, often used to predict leptonic mixing, can lead to the formation of domain walls which can annihilate and generate a stochastic gravitational wave background. We study this phenomenon in three scenarios where the nature of the scalar field responsible for breaking the $A_4$ symmetry spontaneously differs: real, complex, and supersymmetric. For the real scalar, a biased potential produces metastable walls that decay into oscillating two-wall systems with important consequences for gravitational wave signals. In the complex scalar case, we discuss the interplay between domain walls and global strings and classify the types of domain walls that form in terms of the $A_4$ group symmetries. We investigate the properties of supersymmetric $A_4$ domain walls, and highlight the BPS walls. Through a detailed analysis of these models with non-Abelian symmetries, we discover new kinds of domain walls, which we denote as ``oreo''-type composite domain walls, CP-violating domain walls and SUSY non-Abelian domain walls. Finally we show how these results may be achieved in leptonic $A_4$ flavour models, with and without supersymmetry, and discuss their distinctive gravitational wave signatures.

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2 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 1 paper

For some recent work, see, e.g., Refs. [ref] .

Dynamical criterion for biased domain-wall formation · Introduction · 0.99

What it cites · 64 sentences without a confident label

Builds on 1 paper

This setup follows the original Altarelli–Feruglio model of [ref] , but we consider its UV completion by including a heavy lepton superfield pair $(Ê,Ê^c)$ and the right-handed neutrino superfield $ν̂^c$.

Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry · SUSY flavon $A_4$ models · 0.97

Uses the method or tool of 1 paper

For each benchmark, we determine wall profiles between these vacua using a shooting method akin to [ref] .

CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields · $S^c$-type domain walls · 1.00

Uses data or values from 1 paper

Very recently, JUNO released their first measurement of $θ_12$ and $Δm^2_21$ with best-fit values consistent with global data of past experiments and $1σ$ errors less than $1.6%$ and $2.8%$ [ref] .

2511.14593 · Real Flavon $A_4$ Models · 0.82

Compares with 1 paper

This approach is sufficient to obtain qualitative insight into the multi-peak structure generated by multi-scale domain wall collapse, different from the multi-peak structure from multiple degenerate vacua discussed in [ref] .

Non-Abelian Domain Walls and Gravitational Waves · Gravitational Waves from Multi-Scale Domain Wall Collapse · 0.90

Cites as background 20 papers

We consider the flavour symmetry of the lepton sector to be the tetrahedral group $A_4$ [ref] , which is the group of even permutations of four objects.

Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses · Domain Walls from $A_4$ Symmetry · 0.97
In canonical constructions, charged lepton and neutrino mass matrices arise from flavon fields whose vacuum expectation values (VEVs) spontaneously break $A_4$ to its Abelian discrete subgroups, leading to predictive mixing patterns at leading order, the most famous being the tribimaximal (TBM) mixing pattern [ref] .

Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters · Introduction · 0.92
In canonical constructions, charged lepton and neutrino mass matrices arise from flavon fields whose vacuum expectation values (VEVs) spontaneously break $A_4$ to its Abelian discrete subgroups, leading to predictive mixing patterns at leading order, the most famous being the tribimaximal (TBM) mixing pattern [ref] .

Tri-Bimaximal Mixing and the Neutrino Oscillation Data · Introduction · 0.92

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