4D Constructions of Supersymmetric Extra Dimensions and Gaugino Mediation

Abstract

We present 4D gauge theories which at low energies coincide with higher dimensional supersymmetric (SUSY) gauge theories on a transverse lattice. We show that in the simplest case of pure 5D SUSY Yang-Mills there is an enhancement of SUSY in the continuum limit without fine-tuning. This result no longer holds in the presence of matter fields, in which case fine-tuning is necessary to ensure higher dimensional Lorentz invariance and supersymmetry. We use this construction to generate 4D models which mimic gaugino mediation of SUSY breaking. The way supersymmetry breaking is mediated in these models to the MSSM is by assuming that the physical gauginos are a mixture of a number of gauge eigenstate gauginos: one of these couples to the SUSY breaking sector, while another couples to the MSSM matter fields. The lattice can be as coarse as just two gauge groups while still obtaining the characteristic gaugino-mediated soft breaking terms.

Figures (3)

• Figure 1: Mode decomposition for the (a) periodic and (b) orbifold "moose" diagrams. The mass eigenvector expansion is the discrete/latticized analogue of the continuous Fourier expansion. The orbifold $SU(M)^N$ moose diagram is constructed from the $SU(M)^{2N}$ periodic diagram by removing two diametrically opposite links and identifying the sites with their reflection about the reflecting axis.
• Figure 2: One-loop contribution to the MSSM matter scalar masses. The $\bullet$'s on the gaugino line represent the SUSY breaking mass insertion $F/\Lambda$.
• Figure 3: Two-loop gauge-mediated contribution to the MSSM matter scalar masses (only one example diagram shown). The internal loop of dotted lines correspond to the messenger scalars.