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@@ -309,6 +309,7 @@ the numerator of the Green function \cite{Livan_2018_Introduction} gives
1+\frac{p(p-1)}{16}a^{p-2}\alpha_0^2-\frac{\alpha_0\sigma}2+\frac12\log(\alpha_0^2-|\chi_0|^2)
+\frac p4\operatorname{Re}\left(\frac{(p-1)}8\kappa^*\chi_0^2-\epsilon^*\chi_0\right)
\right]\right\}.
+ \nonumber % He's too long, and we don't cite him (now)!
\end{equation}
\end{widetext}
The argument of the exponential has several saddles. The solutions $\alpha_0$