Conformal anomaly for dilaton coupled electromagnetic field

TL;DR

This paper derives the conformal anomaly for dilaton-coupled electromagnetic fields in curved space, highlighting differences from minimal vector and scalar cases, and explaining why an anomaly-induced effective action cannot be constructed.

Contribution

It provides the first derivation of the conformal anomaly for dilaton-coupled electromagnetic fields in curved space and clarifies why an anomaly-induced effective action is not possible.

Findings

Anomaly derived for dilaton-coupled electromagnetic fields in curved space.

Contrasts with minimal vector and scalar cases where effective actions can be constructed.

Explains the impossibility of deriving anomaly-induced effective action for interacting theories like QED.

Abstract

The derivation of the conformal anomaly for dilaton coupled electromagnetic field in curved space is presented. The models of this sort naturally appear in stringy gravity or after spherical reduction of multidimensional Einstein-Maxwell theory. It is shown that unlike the case of minimal vector in curved space or dilaton coupled scalar the anomaly induced effective action cannot be derived. The reason is the same why anomaly induced effective action cannot be constructed for interacting theories (like QED) in curved space.