= Spin-structure obstruction to constant worldsheet supersymmetry
The local rigid <worldsheet supersymmetry> identity $\delta\mathcal L=\partial_\mu J^\mu$ does not by itself prove preservation of every <spin structure>. If $X$ is periodic on a spatial circle and $\psi$ is antiperiodic, a constant $\epsilon$ gives antiperiodic $\delta X=i\bar\epsilon\psi$. It does not preserve the bosonic boundary condition. Compatible periodic fields admit the constant transformation; other sectors must be handled with the local superconformal formulation and their global spin data.
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