For a massless Dirac particle by integrating fermion degree of freedom in path integral, effective action is resulted for gauge field
$$l(\psi,\bar\psi,A)=\bar\psi( \gamma^\mu (i \partial_\mu +A_\mu ) ) \psi $$
$$Z= \int D\psi D\bar\psi D A_\mu e^{(i \int d^3x l)}$$
$$S_{eff} =\int D\psi D\bar\psi e^{(i \int d^3x l)}$$
$$S_{eff} =-i ln (det ( \gamma^\mu (i \partial_\mu +A_\mu )))$$
I want to know:
How can I calculate the following equation?
$$S_{eff} =C_1 C_2 $$
where
$$C_1=- \frac{1}{12} \epsilon^{\mu\nu\rho} \int \frac{d^3p}{(2\pi)^3} tr[ [G(p)\partial_\mu G^{-1}(p)] [G(p)\partial_\nu G^{-1}(p)] [G(p)\partial_\rho G^{-1}(p)] ] $$
and
$$C_2= \int d^3x \epsilon^{\mu\nu\rho}A_\mu \partial_\nu A_\rho $$
$G(p)$ is fermion propagator and $G^{-1}(p)$ is its inverse.