Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-24
Physics
High Energy Physics
High Energy Physics - Theory
11 pages; v2: one formula added, some coefficients corrected
Scientific paper
10.1142/S0217732309030163
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.
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