Non-constant ground states for symmetry-breaking fields in brane world models

TL;DR

This paper derives an approximate analytical solution for the ground state of a bulk scalar field in a brane world model, revealing how boundary conditions and brane separation influence stability and symmetry-breaking.

Contribution

It introduces a novel approximation method for analyzing non-constant ground states in brane world scenarios with symmetry-breaking fields.

Findings

Zero solution stability depends on brane separation.

Approximate solution valid near critical separation.

Boundary conditions exclude constant non-zero solutions.

Abstract

We obtain an approximate analytical solution for the ground state of a bulk scalar field with a double-well potential in the Randall-Sundrum brane world background, in a situation where the boundary conditions rule out a constant field configuration except for the zero solution. The stability of the zero solution is determined by the brane separation. We find our approximation near the critical separation at which the zero solution becomes unstable to small perturbations.