Supersymmetry and the Lorentz fine tuning problem

If physics at the Planck scale requires new conceptions of space-time, renormalizable field theories may generically develop significant violations of Lorentz invariance in the low energy sector. The little recognized “Lorentz fine tuning problem” comes from logarithmic loop corrections which are not suppressed to the enormous extent commonly assumed. Fine-tuning of parameters at the Planck scale is one possible but unpalatable solution. Here we show that violation of Lorentz invariance is highly suppressed in a supersymmetric theory, the Wess-Zumino model. The suppression comes essentially due to the absence of quadratic divergences in the loop corrections. Since quadratic divergences are absent in all supersymmetric theories, our result is not restricted to the Wess-Zumino model. We also obtain an estimate of the Lorentz violation expected due to soft supersymmetry breaking. We conjecture that supersymmetry may be further motivated by yet another fine tuning problem of ordinary quantum field theories.