Classification of Abelian domain walls

Abstract

We discuss domain walls from spontaneous breaking of Abelian discrete symmetries $Z_N$. A series of different domain wall structures are predicted, depending on the symmetry and charge assignments of scalars leading to the spontaneous symmetry breaking (SSB). A widely-existing type of domain walls are those separating degenerate vacua which are adjacent in the field space. We denote these walls as adjacency walls. In the case that $Z_N$ terms are small compared with the $U(1)$ terms, the SSB of $U(1)$ generates strings first and then adjacency walls bounded by strings are generated after the SSB of $Z_N$. For symmetries larger than $Z_3$, non-adjacent vacua exist, we regard walls separating them as non-adjacency walls. These walls are unstable if $U(1)$ is a good approximation. If the discrete symmetry is broken via multiple steps, we arrive at a complex structure that one kind of walls wrapped by another type. On the other hand, if the symmetry is broken in different directions independently, walls generated from the different breaking chains are blind to each other.

15 pages, 6 figures, 2 tables, discussions and refs added, published in PRD

References in corpus (12)

• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse
• Axion cosmology with long-lived domain walls
• Discrete R Symmetries and Domain Walls
• On the four-zero texture of quark mass matrices and its stability
• Axions in the Landscape and String Theory
• Collapsing domain walls beyond $Z_2$
• Correlations between quark mass and flavor mixing hierarchies
• Phenomenological Aspects of Possible Vacua of a Neutrino Flavor Model
• Probing High Scale Dirac Leptogenesis via Gravitational Waves from Domain Walls

Cited by in corpus (9)

• QCD-Collapsed Domain Walls: QCD Phase Transition and Gravitational Wave Spectroscopy
• Friction on ALP domain walls and gravitational waves
• Gravitational waves from cosmic strings in Froggatt-Nielsen flavour models
• Non-Abelian Domain Walls and Gravitational Waves
• Fundamental quantum limits for detecting ultrahigh frequency gravitational waves
• ${\mathbb{Z}}_n$ symmetry broken supersolid in spin-orbit-coupled Bose-Einstein condensates
• Primordial Black Holes from Spatially Varying Cosmological Constant Induced by Field Fluctuations in Extra Dimensions
• Dynamics of $Z_N$ domain walls with bias directions
• Scalar-induced Neutrinoless Double Beta Decay in $SU(5)$