D8

$\mathcal{L} = \frac{1}{16 \pi G_8}(R + l_8^2 R^{MN} R_{MN} + 2 \Lambda_8) + (D \psi) \gamma^0 \tilde{\psi}$

$D \psi = \gamma^M (\partial_M \psi + \frac{1}{2}\omega_M \psi - \frac{1}{2} \psi \omega_M)$

$\omega_M = \frac{1}{2} {\omega_M}^{JK} \gamma_{JK}$

$\gamma_{JK} = \frac{1}{2}(\gamma_J \gamma_K - \gamma_K \gamma_J)$