Kink solutions in nonlocal scalar field theory models

TL;DR

This paper investigates kink solutions in nonlocal scalar field theories with arbitrary kinetic functions, deriving corrections, energy densities, and reconstructing potentials to understand their properties and behaviors.

Contribution

It introduces a perturbative method to analyze nonlocal scalar field theories, providing analytic expressions and a way to reconstruct potentials from solutions.

Findings

First and second order corrections in nonlocality parameter

Analytic expressions for energy density

Reconstruction of potentials from solutions

Abstract

In this paper, we study in detail various solutions, especially kink ones, in different nonlocal scalar field theories, whose kinetic term is described by an arbitrary non-polynomial analytic function of the d'Alembertian operator, and the potential is chosen either to be quadratic or to allow for the kink-like solution. Using the perturbative method, we find corrections of first and second orders in the nonlocality parameter around local solutions for several form factors and generate analytic expressions for the energy density up to the first order in this parameter. Additionally, we also address an inverse problem, that is, we reconstruct the potential corresponding to the given solution obtaining restrictions for the form factor.