= Chiral proof of rigid worldsheet supersymmetry
{title2=$\delta\mathcal L=i\epsilon_2\partial_-(\psi_1\partial_+X)-i\epsilon_1\partial_+(\psi_2\partial_-X)$}
Let $\partial_\pm=\partial_\tau\pm\partial_\sigma$ and $\mathcal L=\partial_+X\cdot\partial_-X+i\psi_1\cdot\partial_+\psi_1+i\psi_2\cdot\partial_-\psi_2$. For constant Grassmann-odd parameters, set $\delta X=i(\epsilon_2\psi_1-\epsilon_1\psi_2)$, $\delta\psi_1=-\epsilon_2\partial_-X$, $\delta\psi_2=\epsilon_1\partial_+X$. In the first chiral sector the variation of the fermionic term cancels $i\epsilon_2\partial_+\psi_1\cdot\partial_-X$ from the bosonic term, leaving $i\epsilon_2\partial_-(\psi_1\cdot\partial_+X)$. The second sector gives the other <total derivative>. This proves off-shell invariance when the boundary flux vanishes. Closure on <fermions> uses their free <equations of motion>. A constant parameter must also preserve the chosen boundary conditions and <spin structure>.
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