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 R1× S3 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 φ 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 R1× S3 and the total energy is proportional to the inverse radius of S3. We also describe similar bounce dyon solutions in SU(N) Yang-Mills theory on the space R1× S2 with signature (-++). Their energy is proportional to the square of the inverse radius of S2. From the viewpoint of Yang-Mills theory on R1,1× S2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x3-axis.