additional polynomial, but it is an effect of having non-zero $\eta$. This is to be compared with Eq.(\[eq:log\_usual\]) in flat spacetime, where a dimensionless integral which leads to a logarithmic divergence gives no polynomials in external momenta and hence the correspondng CTs are trivial.

What is important is the fact that the quadratic CTs (of the form required) also end up giving a polynomial in $-k\eta$ and hence renormalization can be performed in this limit. But in order to renormalize, we need to determine the (unknown) coefficients of the operators in the CT Lagrangian. In the case of familiar field theory (see pt. (4) after Eq. (\[Pi\_usual\_QFT\])), each individual CT gives a different kind of dependence on the external momenta, on the other hand here, that is not the case, we get a polynomial in external momenta whose coefficients are linear combinations of the coefficients of the operators in the CT Lagrangian. Thus, unlike the case of familiar field theory, even in the case with $-k\eta \ll 1$ but $\eta$ being non-zero, we cannot just look at the expression for dimensionally regulated correlator and read-off the number of CTs required or their forms. Thus, to determine the (unknown) coefficients of 