Lorentz breaking supersymmetry and Horava-Lifshitz-like models

We present a Lorentz-breaking supersymmetric algebra characterized by a critical exponent $z$. Such construction requires a nontrivial modification of the supercharges and superderivatives. The improvement of renormalizability for supersymmetric scalar QED is shown, and the Kählerian effective potentials are calculated in different cases. We also show how the theory flows naturally to the Lorentz symmetric case at low energies.

Figure 1

One-loop gauge field contribution: ${\mathcal{K}}_a$.

Figure 2

Dressed gauge propagator.

Figure 3

One-loop gauge-boson contribution: ${\mathcal{K}}_b$.

Figure 4

One-loop self-interacting contribution.

Figure 5

Dressed boson propagator.

Figure 6

One-loop two-point function, $\overline{\mathrm{\Phi }}(-p)\mathrm{\Phi }(p)$.

Figure 7

One-loop two-point function, $V(-p)V(p)$.