# Spectra of the Type II String theories

The spectrum of the Type II string theory (both IIA and IIB) is given by: \begin{array}{*{20}{c}} \hline & {{\text{Sector}}}& & {{\text{Spectrum}}}& & {{\text{Massless Fields}}} & \\ \hline & {{\text{R}} - \operatorname{R} }& & {{{\mathbf{8}}_s} \otimes {{\mathbf{8}}_s}}& & {{C_0},{C_1},{C_2},{C_3}{C_4},...} & \\ \hline & {{\text{NS}} - {\text{NS}}}& & {{{\mathbf{8}}_v} \otimes {{\mathbf{8}}_v}}& & {{g_{\mu \nu }},{F_{\mu \nu }},\Phi ,...} & \\ \hline & {{\text{R}} - {\text{NS}}}& & {{{\mathbf{8}}_s} \otimes {{\mathbf{8}}_v}}& & {{{\Psi '}_\mu },\lambda ',...} & \\ \hline & {{\text{NS}} - {\text{R}}}& & {{{\mathbf{8}}_v} \otimes {{\mathbf{8}}_s}}& & {{\Psi _\mu },\lambda ,...} & \hline \end{array}

I know that for the Ramond-Ramond fields, the even ones belong to the Type IIB string theory and the odd ones belong to the Type IIA string theory.

But what about the rest? Are they there in both Type II string theories? I think it should be the case, because the choice of the GSO projection is only for the R-R sector.

The NS-NS sector is the same in type IIA and IIB, but the R-NS and NS-R sectors differ. The type IIA theory is non-chiral, so the R-NS and NS-R fields transform in $\mathbf{8}_s \otimes \mathbf{8}_v$ and $\mathbf{8}_v \otimes \mathbf{8}_s'$, where $\mathbf{8}_s$ and $\mathbf{8}_s'$ are the two eight-dimensional spinor representations of $SO(8)$. Type IIB, on the other hand, is a chiral theory where the R-NS and NS-R fields are constructed from the same spinor representation, so $\mathbf{8}_s \otimes \mathbf{8}_v$ and $\mathbf{8}_v \otimes \mathbf{8}_s$.
Similarly, the R-R sector of IIA is given by $\mathbf{8}_s \otimes \mathbf{8}_s'$, while in the IIB case it is given by $\mathbf{8}_s \otimes \mathbf{8}_s$.