Abstract
Constructing an equivalence of the NSR and GS superstring formalisms in a general spacetime background involves relating the 8V, and 8S 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.
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