Carroll limit of one-loop effective action

TL;DR

This paper investigates the Carroll magnetic limit of a one-loop scalar effective action, analyzing divergences and finite parts on static backgrounds, and comparing the resulting effective action to lower-dimensional theories.

Contribution

It introduces a novel analysis of the Carroll limit in quantum effective actions, highlighting differences from classical limits and providing explicit computations of divergences and finite parts.

Findings

Divergent parts can be canceled with local counterterms.

Finite parts relate to lower-dimensional effective actions.

The quantum Carroll limit differs from the classical counterpart.

Abstract

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.