Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity

TL;DR

This paper investigates the role of diffeomorphisms and Weyl transformations in resolving ambiguities in the Fefferman-Graham expansion, elucidating their connection to trace anomalies in effective actions.

Contribution

It introduces a cohomological framework to address the Fefferman-Graham ambiguity and identifies nonlocal terms responsible for trace anomalies.

Findings

Resolved the Fefferman-Graham ambiguity using cohomology.

Linked nonlocal effective action terms to trace anomalies.

Provided a method to eliminate ambiguity in holographic renormalization.

Abstract

Using the Weyl transfomations induced by diffeomorphisms we set up a cohomological problem for the Fefferman-Graham coefficients. The cohomologically nontrivial solutions remove the ambiguity and give the nonlocal terms in the effective action responsible for the trace anomalies.