Spontaneous gauge symmetry breaking in a non-supersymmetric D-brane model

We investigate a D-brane system in which spontaneous gauge symmetry breaking occurs. The system consists of four D3-branes and three anti-D7-branes at C3/Z3 singularity. The singularity is blown up by vacuum expectation values of the states of twisted closed string, whose effects appear as Fayet-Iliopoulos terms in low-energy effective field theory. We derive an effective potential for scalar fields in four-dimensional effective field theory using the technique of superstring world-sheet theory. Since there is no supersymmetry in this system, one-loop masses for some scalar fields are considered. We find some stationary and stable vacua in which the original U(2)×U(1)1×U(1)2×U(3) gauge symmetry is spontaneously broken to U(1)×U(1)′×U(3) gauge symmetry. Both Fayet-Iliopoulos terms and one-loop masses are necessary for the existence of such vacua. We carefully investigate a geometrical aspect of the gauge symmetry breaking. We show that the gauge symmetry breaking is understood as the separation of D3-branes. Some implications to the possibility of low-scale string models are also discussed.