= Solution
The constants specify isotropic, nondispersive <linear response>: $\kappa$ controls <electric polarization>, and $\chi$ controls <magnetization>. Their numerical relation to conventional <electric susceptibility> and <magnetic susceptibility> depends on the signs and field normalization in the action. In the rationalized units used here, the printed action gives the <constitutive relations>
$$
\mathbf D=\mathbf E+\mathbf P=(1-\kappa)\mathbf E,\qquad
\mathbf H=\mathbf B-\mathbf M=(1+\chi)\mathbf B.
$$
Thus its relative <permittivity> and <magnetic permeability> are
$$
\boxed{\varepsilon_r=1-\kappa,\qquad \mu_r=\frac1{1+\chi},\qquad \chi_e=-\kappa,\qquad \chi_m=-\frac{\chi}{1+\chi}.}
$$
Here conventional $\chi_m$ is defined by $\mathbf M=\chi_m\mathbf H$, not by $\mathbf M=\chi_m\mathbf B$. With the alternative repaired action that yields the PDF's target equation, $\varepsilon_r$ is unchanged but $\mu_r=(1-\chi)^{-1}$ and $\chi_m=\chi/(1-\chi)$. In particular, a positive conventional <electric susceptibility> corresponds to negative $\kappa$ in the printed conventions; the problem does not specify signs for these constants.
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