Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

TL;DR

This paper explores the holographic renormalization of foliation-preserving gravity, revealing that the dual field theory is scale invariant but not conformally invariant, with implications for trace anomalies and consistency conditions.

Contribution

It demonstrates that foliation-preserving gravity leads to a dual theory that is only scale invariant, not conformal, and connects trace anomalies to potential inconsistencies with conformal symmetry.

Findings

Dual theory is scale invariant but not conformal.

Holographic trace anomaly predicts Ricci scalar squared term.

Incompatibility with Wess-Zumino consistency if conformal.

Abstract

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.