Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

Abstract

In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by the perturbative approach, we investigate the existence of topological structures in the cuscuton-like model. The structures we study are, first, kink-like configurations in two dimensional spacetime, second, vortex solutions in three dimensional one with gauge field ruled by the Maxwell term. In fact, to show the existence of kink solutions it is needed to introduce a standard dynamics term in the cuscuton-like model. Then, a numerical approach (interpolation method) is used and the solution of the scalar field is presented. On the other hand, for the study of topological vortices, we reorganized the energy density to obtain, for convenience, equations similar to those canonical vortex structures, namely, the Maxwell-Higgs model. In fact, even for this particular case, we observed the existence of structures with localized energy and quantized magnetic flux in a given topological sector. We also show that when the model does not spontaneously break the symmetry, the $(2+1)D$ model only admits the so-called non-topological field solutions.

23 pages, 8 figures, version accepted to PRD

References in corpus (10)

• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Global topological k-defects
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• k-defects as compactons
• Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions
• Dressed Power-law Inflation with Cuscuton
• Phase transitions in the logarithmic Maxwell O(3)-sigma model
• Long range vortex configurations in generalized models with the Maxwell or Chern-Simons dynamics
• Kinks in the relativistic model with logarithmic nonlinearity

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• Exponentially generalized vortex
• Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model
• Radially symmetric scalar field solutions in the presence of cuscuton term