D-Branes and Vacuum Periodicity

The superstring/M-theory suggests the Born-Infeld type modification of the classical gauge field lagrangian. We discuss how this changes topological issues related to vacuum periodicity in the SU(2) theory in four spacetime dimensions. A new feature, which is due to the breaking of scale invariance by the non-Abelian Born-Infeld (NBI) action, is that the potential barrier between the neighboring vacua is lowered to a finite height. At the top of the barrier one finds an infinite family of sphaleron-like solutions mediating transitions between different topological sectors. We review these solutions for two versions of the NBI action: with the ordinary and symmetrized trace. Then we show the existence of sphaleron excitations of monopoles in the NBI theory with the triplet Higgs. Soliton solutions in the constant external Kalb-Ramond field are also discussed which correspond to monopoles in the gauge theory on non-commutative space. A non-perturbative monopole solution for the non-commutative U(1) theory is presented.