Spacetime supercharge from an RNS spin field ($Q_A=\oint e^{-{\varphi }_{\mathrm{gh}}/2}{S}_A$)

In the critical RNS string, a spacetime supersymmetry generator is $Q_A=\oint e^{-{\varphi }_{\mathrm{gh}}/2}{S}_A$. The RNS spin field has weight $5/8$ and the superghost exponential has weight $3/8$, making a weight-one current. The GSO projection ensures the locality needed to act on retained vertex operators. Its operator products generate translations and relate NS sector and R sector states.