I found the following paper online: http://www2.mathematik.hu-berlin.de/publ/pre/2013/P-2014-01.pdf. I also attach a screenshot of the paragraph I am confused by (page 63-64).
What is meant by the statement that when renormalizing the effective action flows in the theory space? I am especially confused why the effective action is expanded in operators which where not part of my theory before. E.g. in the paper $\lambda \phi^4$ is renormalized but suddenly the effective action has terms $\propto \phi^n $.
In my understand of renormalization the effective action $\Gamma(\phi)$ is the Legendre transformed of \begin{equation} W(J)=\int [d \phi] e^{-S_{bare}(\phi)-S_{ct}(\phi)+\phi J} \end{equation} where the countqerterms are are just terms $\propto \frac{1}{\epsilon^n}$ in dimensional regularization ensuring that each Feynman diagram is finite. In some sense they are just constants. So how do they give rise to new operators in $\Gamma( \phi)$.
