Cyclically deformed defects and topological mass constraints

TL;DR

This paper introduces a systematic method for generating cyclically deformed defect structures in scalar field models, revealing new topological mass relations and extending defect deformation techniques.

Contribution

It presents a novel cyclic deformation chain approach for constructing and analyzing defect structures with constrained energies, applicable to kink-like and lump-like solutions.

Findings

Supports simultaneous kink-like and lump-like defects in cyclic chains

Derives topological mass relations involving trigonometric and hyperbolic functions

Generalizes to N-cyclic deformations with analytical calculations

Abstract

A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite localized energy of cyclically generated defects. The idea of obtaining cyclically deformed defects concerns the possibility of regenerating a primitive (departing) defect structure through successive, unidirectional, and eventually irreversible, deformation processes. Our technique is applied on kink-like and lump-like solutions in models described by a single real scalar field, such that extensions to quantum mechanics follow the usual theory of deformed defects. The preliminary results show that the cyclic device supports simultaneously kink-like and lump-like defects into 3- and 4-cyclic deformation chains with topological mass values closed by trigonometric and hyperbolic deformations. In a straightforward generalization, results concerning with the analytical calculation of $N$-cyclic deformations are obtained and lessons regarding extensions from more elaborated primitive defects are depicted.