Yang-Mills instanton on a four dimensional wormhole: asymptotic stability in the energy space

TL;DR

This paper studies the stability of a Yang-Mills instanton in a 4+1 dimensional wormhole spacetime, demonstrating its conditional asymptotic stability under small odd perturbations in the energy space.

Contribution

It establishes the conditional asymptotic stability of a Yang-Mills instanton in a wormhole spacetime under small odd perturbations, extending stability analysis to higher-dimensional curved backgrounds.

Findings

The instanton is conditionally asymptotically stable in the odd energy space.

Small odd perturbations decay over time, preserving the instanton's structure.

The analysis reduces the problem to a one-dimensional nonlinear wave equation.

Abstract

In this paper we consider an $SU(2)$ Yang-Mills field propagating in the $4+1$ dimensional wormhole spacetime. Assuming the spherically symmetric magnetic ansatz the problem reduces to a one dimensional non linear wave equation. This equation posses a degree one solution (instanton) which is odd in space. We consider small, odd perturbations of the instanton and show that it is conditionally asymptotically stable in the odd energy space.