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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.

String theories with worldsheet fermionic degrees of freedom and the corresponding supersymmetric consistency conditions. In the RNS string description, consistent supersymmetric GSO projections produce spacetime supersymmetry and remove the NS tachyon. The flat critical dimension is ten. Worldsheet supersymmetry alone does not guarantee spacetime supersymmetry without a suitable projection.

Before the GSO projection, the Neveu–Schwarz sector has string oscillator levels $0,1/2,1,3/2$, with physical multiplicities $1,8,36,128$ in ten-dimensional light-cone gauge in string theory. The eight transverse worldsheet Majorana fermions supply eight single ${\psi }_{-1/2}$ states. Level one has eight ${\alpha }_{-1}$ states and $\left(\genfrac{}{}{0ex}{}{8}{2}\right)=28$ pairs of distinct ${\psi }_{-1/2}$ modes. Level $3/2$ has $8$ single ${\psi }_{-3/2}$ modes, $8\cdot 8$ mixed boson–fermion modes and $\left(\genfrac{}{}{0ex}{}{8}{3}\right)=56$ triples. Their squared masses are respectively $-1/(2{\alpha }^{\prime }),0,1/(2{\alpha }^{\prime }),1/{\alpha }^{\prime }$. In the Ramond sector, the Ramond zero-mode Clifford algebra gives a sixteen-dimensional ground space. At level one, ${\alpha }_{-1}^i$ and ${\psi }_{-1}^i$ each provide $8\cdot 16$ states, hence multiplicities $16,256$ at squared masses $0,1/{\alpha }^{\prime }$. No half-integer Ramond levels occur. The GSO projection keeps odd NS fermion number and one total Ramond chirality, giving $8$ bosons and $8$ fermions at zero mass, then $128$ of each at the first massive level.