  We study the dependence on field parametrization of the functional
renormalization group equation in the $f(R)$ truncation for the effective
average action. We perform a systematic analysis of the dependence of fixed
points and critical exponents in polynomial truncations. We find that, beyond
the Einstein-Hilbert truncation, results are qualitatively different depending
on the choice of parametrization. In particular, we observe that there are two
different classes of fixed points, one with three relevant directions and the
other with two. The computations are performed in the background approximation.
We compare our results with the available literature and analyze how different
schemes in the regularizations can affect the fixed point structure.
