From sine-Gordon to vacuumless systems in flat and curved spacetimes

Abstract

In this work we start from the Higgs prototype model to introduce a new model, which makes a smooth transition between systems with well-located minima and systems that support no minima at all. We implement this possibility using the deformation procedure, which allows the obtaining a sine-Gordon-like model, controlled by a real parameter that gives rise to a family of models, reproducing the sine-Gordon and the so-called vacuumless models. We also study the thick brane scenarios associated with these models and investigate their stability and renormalization group flow. In particular, it is shown how gravity can change from the 5-dimensional warped geometry with a single extra dimension of infinite extent to the conventional 5-dimensional Minkowski geometry.

Quasinormal modes in kink excitations and kink–antikink interactions: a toy model

“…The authors studied the kink-antikink interactions when the normal modes of the latter model ( = 0) turn into the QNMs of the former one ( = 0). This "volcano shaped" linear stability potentials also appear in other models such as vacuumless systems [69] and kinks with power-law asymptotics [66]. In the present work with our generic simplified stability potentials we plan to capture the essential aspects of the kink excitations and the kink-antikink interactions when a normal mode of a soliton gradually turns into a QNM.…”

Analytical study of kinklike structures with polynomial tails

“…In (1, 1) spacetime dimensions, in particular, there are scalar field models that support localized structures known as kinks, which appear due to the set of degenerate minima that characterize the several topological sectors of the systems. Each topological sector provides a kink-antikink pair of solutions, which has been explored in several scenarios; see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

“…Each topological sector provides a kink-antikink pair of solutions, which has been explored in several scenarios; see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

BPS states for scalar field theories based on $$ \mathfrak{g} $$2 and $$ \mathfrak{su} $$(4) algebras

“…to have a topological charge associated to it, and to leave a specific functional of the field and its first derivatives (which can coincide with the static energy functional of that theory) stationary. This observation leads not only to a satisfactory explanation on why the "Bogomolny trick" works but also it gives a fundamental recipe to the construction of new BPS models [16][17][18].…”