Is there any simple expression for this in general $D$-dimensions?
$$\sum_b(\gamma_a^{\;b})_{\alpha\beta}(\gamma_b^{\;c})_{\rho\delta}$$
where $\gamma^a$ are the usual $D$-dimensional gamma matrices and $\gamma^{ab}= \frac{1}{2}[\gamma^a,\gamma^b]$. The others are defined by Clifford algebra.
I have searched for lots of identities from Clifford Algebra like Fierz identities but they don't seem to be helpful.