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

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 ϕ, 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 ϕ=0 of the potential, bounces off the potential wall and returns to ϕ=0. The gauge field tensor components parametrized by ϕare 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.