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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?

Qmechanic
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Logan R. Kearsley
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Yang-Mills theory is IR free in $D \geq 5$ dimensions. So at low energies any such theory is non-interacting: in particular there are no bound states of quarks. Moreover, it's not clear how to "construct" $D \geq 5$ nonabelian gauge theory at short distances - you can't just take the continuum limit. This just means that any such theory can only arise as a low-energy approximation of a UV theory that has more degrees of freedom. If anything, QCD in $D=4$ is qualitatively pretty close to the situation in $D=3$, and to a lesser extent to QCD in $D=2$.

Hans Moleman
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