Abstract
The relationship between spin structures and superworldsheet topology is shown by the construction of superworldsheets in which the anticommuting coordinates of different coordinate patches are stitched together in non-trivial ways. The four spin structures of the NSR string, corresponding to R-R, NS-NS, NS-R and R-NS boundary conditions are shown to arise as a consequence of topology. More interesting is the existence of more complicated twisted spin structures for the NSR string with N=2 worldsheet supersymmetry. This class of spin structures is also shown to exist for the heterotic string when its heterotic fermions are endowed with a bundle structure. The transformation of spin structures under field redefinitions and modular transformations are examined. Finally the spin structures associated with the ghost sector of the heterotic string are explored.
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