It was pointed out as a comment on my question on atomic physics in higher dimensions that that question implicitly rests on an assumption that QCD, and thus the structure of atomic nuclei, is pretty much unchanged in higher dimensions. That seems a reasonable assumption to me, based on my admittedly extremely sketchy knowledge of QCD (which might reasonably be summarized as "gluon-mediated forces between quarks act like springs, so dimensionality doesn't matter"), but it is indeed an assumption. While there is plenty of internet-accessible discussion on the effects on electromagnetism when moving into higher dimensions, cursory searching on my part was only able to turn up two papers on higher-dimension QCD, neither of which address the structure of nucleons or nuclei.
So, what does happen to QCD in higher dimensions? Do we still get neutrons and protons in 4+1, 5+1, or higher-dimensional spacetimes, or does stuff get Weird?