= Level-two open-string polarization decomposition
{title2=$\zeta_{\mu\nu}=\frac{t}{20}(3q_\mu q_\nu+\eta_{\mu\nu})+q_\mu A_\nu+q_\nu A_\mu+c_{\mu\nu}$}
For $d=26$, $q^2=-2$ and the <physical string state> $[\zeta_{\mu\nu}\alpha_{-1}^\mu\alpha_{-1}^\nu+b_\mu\alpha_{-2}^\mu]|p\rangle$, the <Virasoro constraints> give $b_\nu=-q^\mu\zeta_{\mu\nu}$ and $t=\zeta^\mu{}_{\mu}=-2q\cdot b$. Every solution has the displayed decomposition, where $q\cdot A=0$ and $c$ is symmetric, traceless and transverse to $q$. The vector piece is $L_{-1}(2A\cdot\alpha_{-1}|p\rangle)$; the scalar piece is $t(L_{-2}+3L_{-1}^2/2)|p\rangle/10$. These are <null string states>, leaving the transverse traceless massive tensor as the physical polarization.
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