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Witten's 1981 paper "Search for a realistic Kaluza-Klein theory" is frequently cited for its observation that, in a compactification of d=11 supergravity on a manifold with SU(3) x SU(2) x U(1) isometry, left-handed and right-handed fermions would transform in the same way under the gauge group, in opposition to experiment. Years later, in the era of M-theory, Acharya and Witten were able to get chiral fermions by compactifying on a manifold with singularities. But Witten 1981 also mentioned, at the end, that coupling to a torsion field might produce chiral asymmetry. (Subsequent explorations of the idea: for and against.)

Now I'm wondering: Can torsion in M-theory revive the 1970s version of Kaluza-Klein theory? A very recent paper constructed CFT duals for M-theory on AdS4 x M111 with torsion flux, M111 being one of the "Mpqr manifolds" with SU(3) x SU(2) x U(1) isometry group that was considered in Witten 1981. (The Mpqr notation is Witten's; in a more recent notation this manifold is designated M3,2 or sometimes Y2,3.) Can M-theory on such a background give rise to chiral fermions?

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    $\begingroup$ Good links. I am afraid that you found expert enough papers that you would have to ask their authors to stage a battle here instead of asking someone else. ;-) Did Wu and Zee really say that they can't get chirality? It looks that they only say that they don't get the right representations. $\endgroup$ – Luboš Motl May 25 '11 at 10:47
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    $\begingroup$ "We conclude that with the introduction of torsion, Kaluza-Klein theories can have massless fermions, but not chiral fermions." $\endgroup$ – Mitchell Porter May 29 '11 at 5:15

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