Question

Chiral fermions from torsion flux in M-theory?

Answer 1

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.)

Hope it helps you.

Answer 2

Explanation:

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 backgrou