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 × 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 ℝ × 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 ℝ × 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.