Soft breaking of the ℤ₂ symmetry in the ϕ⁴ theory

2025/07/04 by F. C. E. Lima, C. A. S. Almeida, Lima, F. C. E. +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.2507.03270

openalex publication_date 2025/07/04 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

We consider a two-dimensional scalar field theory that modifies the standard ϕ⁴ model by introducing a smooth breaking of translational invariance through a hyperbolic generalizing function. This function explicitly breaks the ℤ₂ symmetry; however, it also introduces a mechanism capable of generating new energy minima (vacua) and of localizing or delocalizing field fluctuations around these vacua. Thus, this mechanism enables the continuous transformation of the kink/antikink-like configurations into compacted asymmetric double-kink/antikink structures. Accordingly, this transformation gives rise to new classes of configurations resembling asymmetric non-topological solitons, characterized by a soft breaking of the ℤ₂ symmetry. These findings are particularly compelling, as they are consistent with results describing Su-Schrieffer-Heeger (SSH) domain walls in dimerized polymer systems.

Citations

• k-Inflation
• Topology of cosmic domains and strings
• Radiative Corrections as the Origin of Spontaneous Symmetry Breaking
• Radiative Corrections as the Origin of Spontaneous Symmetry Breaking

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