Universality and ambiguity in fermionic effective actions

TL;DR

This paper explores the ambiguity in the finite part of the one-loop effective action for massive fermions, revealing a non-local multiplicative anomaly due to non-universal finite contributions despite universal UV divergences.

Contribution

It introduces the concept of non-local multiplicative anomaly in fermionic effective actions and formulates criteria for its existence across different external fields.

Findings

Finite parts of fermionic effective actions are non-universal due to multiplicative anomalies.

Universal UV divergences do not imply universality of the finite effective action.

Criteria for the existence of multiplicative anomalies are established.

Abstract

We discuss an ambiguity in the one-loop effective action of massive fields which takes place in massive fermionic theories. The universality of logarithmic UV divergences in different space-time dimensions leads to the non-universality of the finite part of effective action, which can be called the non-local multiplicative anomaly. The general criteria of existence of this phenomena are formulated and applied to fermionic operators with different external fields.