Direct mediation of metastable supersymmetry breaking

The supersymmetric $\mathrm{SU}(N_C)$ Yang-Mills theory coupled to $N_F$ matter fields in the fundamental representation has metastable vacua with broken supersymmetry when $N_C<N_F<\frac{3}{2}{N}_C$. By gauging the flavor symmetry, this model can be coupled directly to the standard model. We show that it is possible to make a slight deformation to the model so that gaugino masses are generated and the Landau pole problem can be avoided. The deformed model has simple realizations on intersecting branes in string theory, where various features of the metastable vacua are encoded geometrically as brane configurations.

Figure 1

One-loop effective potential $V_{\mathrm{eff}}(\widehat{\Phi }/\overline{m})$ along the real axis of $\widehat{\Phi }$ for $\mathrm{Re}[\mathrm{Tr}\delta \widehat{\chi }]=0$, $m_z=\overline{m}/3$, and $\mu =\overline{m}/100$. The critical point is at $\widehat{\Phi }=0.1747\overline{m}$. At $\widehat{\Phi }\sim 3\overline{m}$ there is a tachyonic direction toward nonzero $\rho$, $\tilde{\rho }$, $Z$, and $\tilde{Z}$ in field configuration space.

Figure 2

The electric brane configuration.

Figure 3

The brane configuration for the ISS vacuum in the deformed ISS model.

Figure 4

The brane configuration for the metastable vacua with lower energies.