Someone could publish a paper tomorrow saying, "This choice of Calabi-Yau manifold recovers the physics of the observed universe, and implies this feasible way to detect how the universe's string-theoretic nature differs from vanilla GR+QFT". The first part is unlikely to happen soon, if only because there are so many choices of Calabi-Yau space to consider, some of which have already been shown to predict a different universe. But this question focuses on the second part. Are there any known examples, however alien the results may be compared with what we see, that meet the following criterion?
If that choice were correct in some universe, that universe would look like GR (or a suitable alternative classical theory of gravity) plus QFT (with a suitable particle zoo, parameters etc. that would be that universe's "standard model") in appropriate low-energy limits, but string-theoretic corrections would be observable under suitable conditions?
In particular, I'm hoping for an example where the specific beyond-ST limits have been computed, and we can imagine physicists in that universe discovering those first and then realizing how to observationally merit ST with that choice of a CY manifold.
Effectively, this question inverts a common way of thinking about experimental probes of ST. Instead of searching the landscape for something that looks like us, we choose a starting point, imagine being in that universe, then wonder whether, should local physicists correctly guess the chosen starting point, they could feasibly test it. I don't know much about the classification of CY manifolds, but I imagine some "simple" ones make for easier calculations, albeit not necessarily ones that make string-theoretic corrections to the low-energy limit easier to access. I'm hoping at least one researcher has tried this, with the motive of illustrating that string theory could be easily tested in some part of the landscape, even if our own Universe doesn't make it easy.