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

## TL;DR

This paper introduces a family of models interpolating between sine-Gordon and vacuumless systems using a deformation method, and explores their implications in thick brane scenarios, including stability and gravitational geometry transitions.

## Contribution

It presents a novel deformation approach to generate models transitioning from well-minimized to non-minimized systems, with applications to thick brane and gravitational geometry.

## Key findings

- Reproduces sine-Gordon and vacuumless models via deformation.
- Analyzes stability and renormalization group flow of brane scenarios.
- Shows gravity transitions from warped to Minkowski geometry.

## 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 obtention of 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, one shows 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.