Spontaneous Gauge Symmetry Breaking in a Non-Supersymmetric D-brane Model

TL;DR

This paper studies spontaneous gauge symmetry breaking in a non-supersymmetric D-brane system, deriving an effective potential and analyzing stable vacua where gauge symmetry is broken via brane separation.

Contribution

It provides a detailed analysis of gauge symmetry breaking in a non-supersymmetric D-brane setup, including the derivation of the effective potential and the role of Fayet-Iliopoulos terms and one-loop masses.

Findings

Stable vacua with broken gauge symmetry identified

Gauge symmetry breaking corresponds to D3-brane separation

Both FI terms and one-loop masses are essential for vacua stability

Abstract

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 C^3/Z_3 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) x U(1)_1 x U(1)_2 x U(3) gauge symmetry is spontaneously broken to U(1) x U(1)' x 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.