Nowhere-vanishing spinors and topological obstructions to the equivalence of the NSR and GS superstrings

Constructing an equivalence of the NSR and GS superstring formalisms in a general spacetime background involves relating the 8_V, and 8_S representations with the aid of a nowhere-vanishing Majorana-Weyl spinor on the eight-dimensional transverse space. The authors discuss the possibility of a global obstruction to the existence of such spinor fields and show that a necessary and sufficient condition for this to be absent is the vanishing of a certain linear combination of the characteristic classes of the spacetime.