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

2025/11/18 by Kowalczyk, Michał, Monreal, Javier
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.14880

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.

Citations

• Classification of kink clusters for scalar fields in dimension 1+1
• Multisoliton solutions for equivariant wave maps on a 2+1 dimensional wormhole
• Asymptotic stability and classification of multi-solitons for Klein-Gordon equations
• Soliton resolution for energy-critical wave maps in the equivariant case
• A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models
• Soliton resolution for the radial critical wave equation in all odd space dimensions
• Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line
• Strichartz estimates for the one-dimensional wave equation
• Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes
• Stable soliton resolution for exterior wave maps in all equivariance\n classes
• Classification of radial solutions of the focusing, energy-critical wave equation

Related

• Black Holes and Abelian Instantons
• Stable regular solution of Einstein-Yang-Mills equation
• Instantons, Euclidean wormholes and AdS/CFT
• Classical stability of stringy wormholes in flat and AdS spaces
• The exact solutions to two-dimensional Yang-Mills theory: su(2) and u_⋆(1)