Neveu–Schwarz level operator ($N_{\mathrm{NS}}={\sum }_{k>0}{\alpha }_{-k}\cdot {\alpha }_k+{\sum }_{r>0}r{b}_{-r}\cdot b_r$)

Before the GSO projection, $N={\sum }_{k>0}{\alpha }_{-k}\cdot {\alpha }_k+{\sum }_{r>0}r{b}_{-r}\cdot b_r$ takes nonnegative half-integer values. The first vector at $N=1/2$ is massless for string intercept $a_{\mathrm{NS}}=1/2$.