# Complex time theories with spacetime $\mathbb{R}^3\times\mathbb{C}$

Are there any well-developed (string?..) theories assuming that, what we perceive as a (3+1) Minkowskian manifold, is a projection/compactification of a 5-dim spacetime, locally obtained via complexification of the usual time? And this additional imaginary time direction is also the one we use for Wick rotation in QFT 🙃