Abstract
We consider fermions in theories of higher dimensional gravity where the four-dimensional gauge group is embedded in the invariance group of d dimensional ( d>4) Lorentz and general co-ordinate transformations. It is a necessary condition for obtaining massless chiral fermions from dimensional reduction that the d dimensional spinor does not admit a mass term consistent with Lorentz and general co-ordinate transformations. This is the case for a Weyl spinor for d = 6 8 mod 8, a Majorana spinor for d = 9 mod 8 or a Majorana-Weyl spinor for d = 2 mod 8.
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