Majorana-Weyl spinor (${\Gamma }_{\ast }\psi =\pm \psi ,{\psi }^c=\psi$)

A Majorana-Weyl spinor satisfies both a Majorana spinor reality condition and a Weyl spinor chirality condition when dimension and signature permit them. In ten-dimensional Lorentzian spacetime it has sixteen real components off shell and eight physical massless spin-one-half polarizations.