The opinion is spreading that the real discovery of the LHC was that the Higgs boson mass is special. The most impressive prediction was Shaposhnikov and Wetterich 2006, which got the right value from the assumption that gravity is asymptotically safe.
This creates cognitive dissonance for anyone who appreciates the string-theoretic model of quantum gravity. Asymptotic safety isn't even consistent with the holographic principle, is it?
Well, asymptotic safety is one of several heterodox approaches to quantum gravity in which the dimension of spacetime seems to change from 4 to 2 at the smallest scales. Sabine Hossenfelder lists a few others and says, "It is difficult to visualize what is happening with the dimensionality of space if it goes down continuously, rather than in discrete steps".
Fractals can have non-integer dimensionality. But they are typically embedded in a larger space. Meanwhile, in string theory, one has a 2d worldsheet embedded in a "target space" that usually has more than two dimensions. So what if the world sheet embeds in the target space as a multifractal surface that is 4d on large scales but 2d on small scales?