Level-two scalar Virasoro null state ($|Z⟩=(L_{-2}+\frac{3}{2}{L}_{-1}^2)|p⟩$)

For $L_0|p⟩=-|p⟩$, the descendant $Z=(L_{-2}+\frac{3}{2}{L}_{-1}^2)|p⟩$ obeys $L_{1}Z=0$ and $L_{2}Z=(D-26)|p⟩/2$. It becomes physical and null at 26 and supplies the scalar quotient needed for the massive spin-two light-cone gauge in string theory spectrum.