Consistency conditions and trace anomalies in six dimensions

TL;DR

This paper systematically classifies all trace anomalies in six-dimensional conformal field theories, distinguishing true anomalies from trivial ones and providing explicit expressions for the latter.

Contribution

It identifies all 10 solutions to the consistency conditions in d=6, clarifies which are true anomalies, and explicitly derives the trivial anomalies from local functionals.

Findings

4 true anomalies: 1 type A and 3 type B

6 trivial anomalies obtained from local functionals

Explicit expressions for all trivial anomalies provided

Abstract

Conformally invariant quantum field theories develop trace anomalies when defined on curved backgrounds. We study again the problem of identifying all possible trace anomalies in d=6 by studying the consistency conditions to derive their 10 independent solutions. It is known that only 4 of these solutions represent true anomalies, classified as one type A anomaly, given by the topological Euler density, and three type B anomalies, made up by three independent Weyl invariants. However, we also present the explicit expressions of the remaining 6 trivial anomalies, namely those that can be obtained by the Weyl variation of local functionals. The knowledge of the latter is in general necessary to disentangle the universal coefficients of the type A and B anomalies from calculations performed on concrete models.