Connecting holographic Wess-Zumino consistency condition to the holographic anomaly

Abstract

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

Gravitational path integral from the T 2 deformation

“…of (2.25) to satisfy certain Wess-Zumino consistency conditions, see e.g. [56,57]. We will see in the following section that adding the Ricci potential as in (2.5) with a specific coefficient solves part of the problem, namely it turns the exponential into a path-independent diffinvariant object.…”

Anomalies in gravitational charge algebras of null boundaries and black hole entropy

“…See[58] for a discussion of the Wess-Zumino consistency condition in the context of holographic Weyl anomalies.…”

Finite cutoff AdS5 holography and the generalized gradient flow

“…This consequently implies that the addition of a special subset of irrelevant operators doesn't trigger an infinite number of other more irrelevant operators thereby leading to a proliferation of scales. More generally, the codification of emergent of bulk diffeomorphism invariance in local Holographic RG flows is through what is called the holographic Wess-Zumino consistency condition [35].…”