Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints

Abstract

We investigate a class of models described by two real scalar fields in two-dimensional spacetime. The study focuses mainly on the presence of exact static solutions which satisfy the first-order formalism, in models constructed to engender Lorentz symmetry violation. We start by exploring a direct connection between Lorentz breaking and geometric constraint, as experimentally examined in the case of domain walls in geometrically constrained magnetic materials. By means of a specific choice of functions, we show that imposing geometric constraint within the Lorentz-violating framework recovers the exact solutions of the corresponding Lorentz-invariant theory. Furthermore, we extend the investigation to new models that go beyond reproducing the Lorentz invariant geometrically constrained solutions, revealing that it remains possible to parametrize the first-order equation of one of the fields through a suitably redefined coordinate.

12 pages, 9 figuras; new version

References in corpus (44)

• Testing General Relativity with Present and Future Astrophysical Observations
• Data Tables for Lorentz and CPT Violation
• Time crystals: a review
• Classical Time Crystals
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Solitons in systems of coupled scalar fields
• Generalized Global Defect Solutions
• A Bogomol`nyi equation for intersecting domain walls
• On Lorentz violation in Horava-Lifshitz type theories
• Physical Instances of Noncommuting Coordinates
• Degenerate Domain Wall Solutions in Supersymmetric Theories
• Magnetic domain walls in constrained geometries
• Soliton Stability in Systems of Two Real Scalar Fields
• Domain Walls as Dark Energy
• Spectral Walls in Soliton Collisions
• Collective coordinate model of kink-antikink collisions in ${\varphi }^4$ theory
• Defect Structures in Lorentz and CPT Violating Scenarios
• Tiling the plane without supersymmetry
• Lorentz violation in Dirac and Weyl semimetals
• Resonance structures in coupled two-component ${\varphi }^4$ model
• Kink Moduli Spaces -- Collective Coordinates Reconsidered
• Improved bounds on Lorentz violation from composite-pulse Ramsey spectroscopy in a trapped ion
• Geometrically Constrained Kinklike Configurations
• From Early Theories of Dzyaloshinskii-Moriya Interactions in Metallic Systems to Today's Novel Roads
• Lorentz-violating effects on topological defects generated by two real scalar fields
• Vacuum defects without a vacuum
• Topological solitons in a vacuumless system
• Quantum field theory based on birefringent modified Maxwell theory
• The BPS property and its breaking in 1+1 dimensions
• Spectral walls in multifield kink dynamics
• Multikink scattering in the ${\varphi }^6$ model revisited
• Magnetic-conductivity effects on electromagnetic propagation in dispersive matter
• Sigma Model Q-balls and Q-Stars
• Spectral walls in antikink-kink scattering in the ${\varphi }^6$ model
• Global Defects In Theories With Lorentz Symmetry Violation
• Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics
• Kink scattering in the presence of geometric constrictions
• Geometrically constrained multifield models with BNRT solutions
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Wobbling kinks and shape mode interactions in a coupled two-component ${\varphi }^4$ theory
• Some of the many uses of scalar fields: kinks, lumps, and geometric constraints
• Properties of Non-topological Solitons in Two-dimensional Model With Resurrected Conformal Symmetry
• Localized structures in three-field models: geometrically constrained configurations and the first-order framework
• Discrete time crystals detected by time-translation twist