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

TL;DR

This paper demonstrates how the Holographic Wess--Zumino consistency conditions, when mapped to Hamiltonian systems, lead to the holographic anomaly and characterize theories with local gravity duals, especially in four dimensions.

Contribution

It establishes a direct connection between HWZ consistency conditions and the holographic anomaly, highlighting their role in identifying theories with local gravity duals.

Findings

HWZ conditions lead to holographic anomaly

Equality of a and c anomaly coefficients in 4D CFTs

HWZ conditions characterize theories with local gravity duals

Abstract

The Holographic Wess--Zumino (HWZ) consistency conditions are shown through a step by step mapping of renormalization group flows to Hamiltonian systems, to lead to the Holographic anomaly. These conditions codify 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 conditions leads to the latter relation between anomaly coefficients adds evidence to the claim that the HWZ conditions are a defining feature of theories possessing local gravity duals.