Carroll limit of a one-loop effective action

In this paper, we consider a Carroll magnetic limit of a one-loop scalar effective action. We work on general static backgrounds and compute both divergent and finite parts of the effective action in this limit. We show that the divergent part can be removed by adding local counterterms. The finite part is related to an effective action in a lower dimensional theory which however does not coincide in general with the one obtained by a Carroll limit in the classical counterpart.