= Unprojected low levels of the open RNS string
{title2=$\alpha'M^2\leq1$}
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 $\binom82=28$ pairs of distinct $\psi_{-1/2}$ modes. Level $3/2$ has $8$ single $\psi_{-3/2}$ modes, $8\cdot8$ mixed <boson>–<fermion> modes and $\binom83=56$ triples. Their squared masses are respectively $-1/(2\alpha'),0,1/(2\alpha'),1/\alpha'$. 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 $8\cdot16$ states, hence multiplicities $16,256$ at squared masses $0,1/\alpha'$. 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.
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