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The Holographic Wess--Zumino (HWZ) consistency conditions are shown through astep by step mapping of renormalization group flows to Hamiltonian systems, tolead to the Holographic anomaly. These conditions codify how the energy scale,when treated as the emergent bulk direction in Holographic theories, is put onequal footing as the other directions of the space the field theory inhabits.So, this is a defining feature of theories possessing local Holographic bulkduals. In four dimensional Holographic conformal field theories, the $a$ and$c$ anomaly coefficients are equated, and this is seen as a defining propertyof theories which possess General Relativity coupled to matter as a dual.Hence, showing how the former consistency conditions leads to the latterrelation between anomaly coefficients adds evidence to the claim that the HWZconditions are a defining feature of theories possessing local gravity duals.

Connecting Holographic Wess--Zumino Consistency Conditions to the Holographic Anomaly