Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory

TL;DR

This paper constructs and analyzes bounce and dyon solutions in SU(N) Yang-Mills theory on curved spaces, revealing their energy dependence on the geometry and their interpretation as flux tubes.

Contribution

It introduces explicit bounce and dyon solutions in SU(N) Yang-Mills theory on R^1×S^3 and R^1×S^2, connecting them to matrix models and flux tube configurations.

Findings

Classical bounce solutions in SU(N) Yang-Mills on R^1×S^3.

Dyon solutions with energy proportional to inverse radius squared.

Interpretation of solutions as non-Abelian flux tubes.

Abstract

We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski signature (-+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills equations are reduced to the equation of a particle moving in the double-well potential. The classical solution is a bounce, i.e. a particle which begins at the saddle point \phi=0 of the potential, bounces off the potential wall and returns to \phi=0. The gauge field tensor components parametrized by \phi are smooth and for finite time both electric and magnetic fields are nonvanishing. The energy density of this non-Abelian dyon configuration does not depend on coordinates of R^1\times S^3 and the total energy is proportional to the inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N) Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy is proportional to the square of the inverse radius of S^2. From the viewpoint of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x^3-axis.