Consistency conditions and trace anomalies in six dimensions

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.

16 pages, LaTeX

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• The General 3-Graviton Vertex ($TTT$) of Conformal Field Theories in Momentum Space in $d=4$
• On the trace anomaly of a Weyl fermion
• Einstein Gravity from Conformal Gravity in 6D
• Black strings with negative cosmological constant: inclusion of electric charge and rotation
• Not Conformally-Einstein Metrics in Conformal Gravity
• Weyl Anomaly Induced Stress Tensors in General Manifolds
• Simple recipe for holographic Weyl anomaly
• Integration of trace anomaly in 6D
• One-Loop Divergences in 6D Conformal Gravity
• Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle
• Search for flow invariants in even and odd dimensions
• Simplified Method for Trace Anomaly Calculations in d=6 and d<6
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Casimir effect and thermodynamics of horizon instabilities
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS
• 7D Randall-Sundrum cosmology, brane-bulk energy exchange and holography
• Casimir energy on the sphere and 6D CFT trace anomaly