Ramond level operator ($N_R$)

For integer transverse string modes, $N_R={\sum }_{k>0}({\alpha }_{-k}\cdot {\alpha }_k+k{d}_{-k}\cdot d_k)$ with vacuum-annihilating normal ordering. Each nonzero-mode creation operator raises the level by $k$; fermionic zero modes commute with it. The open-string mass condition is $M^2=2\pi T{N}_R$, with zero Ramond intercept.