Dynamical Generation of Spacetime Signature by Massive Quantum Fields on   a Topologically Non-Trivial Background
  The effective potential for a dynamical Wick field (dynamical signature) induced by the quantum effects of massive fields on a topologically non-trivial $D$ dimensional background is considered. It is shown that when the radius of the compactified dimension is very small compared with $\Lambda^{1/2}$ (where $\Lambda$ is a proper-time cutoff), a flat metric with Lorentzian signature is preferred on ${\bf R}^4 \times {\bf S}^1$. When the compactification radius becomes larger a careful analysis of the 1-loop effective potential indicates that a Lorentzian signature is preferred in both $D=6$ and $D=4$ and that these results are relatively stable under metrical perturbations. 
Sergei D. Odintsov, August Romeo and Robin W. Tucker