= Rigid worldsheet supersymmetry boundary term
{title2=$\delta\mathcal L=\partial_\mu J^\mu$}
In flat <conformal gauge>, take $\mathcal L=\partial X\cdot\partial X+i\alpha'\bar\psi\gamma^\mu\partial_\mu\psi$ and rigid transformations $\delta X=iA\bar\epsilon\psi$, $\delta\psi=B\gamma^\nu\partial_\nu X\epsilon$, with $A=\alpha'B$. The <Majorana Grassmann bilinear interchange> and <Clifford algebra> combine the variations into
$$
\delta\mathcal L=\partial_\mu\bigl(iA\partial_\nu X\cdot\bar\epsilon\gamma^\mu\gamma^\nu\psi\bigr).
$$
The identity is off shell. The integrated action is invariant when its boundary flux vanishes, for example on a closed worldsheet or with compatible supersymmetric endpoint conditions. Constant spinors and ordinary derivatives here refer to flat gauge; arbitrary curved worldsheets require covariant spinor derivatives and the locally supersymmetric completion.
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