Holographic Two-Point Functions in Conformal Gravity

TL;DR

This paper computes two-point functions in holographic conformal gravity, revealing the structure of energy-momentum and partially massless response operators, and discusses the theory's unitarity.

Contribution

It provides explicit calculations of two-point functions for EM and PMR operators in 4D conformal gravity, clarifying their structure and symmetry properties.

Findings

Two-point function of EM is transverse and traceless.

Two-point function of PMR has two parts, for tensor and vector operators.

Correlation of EM with PMR is zero, consistent with conformal symmetry.

Abstract

In this paper we compute the holographic two-point functions of four dimensional conformal gravity. Precisely we calculate the two-point functions for Energy- Momentum (EM) and Partially Massless Response (PMR) operators that have been identified as two response functions for two independent sources in the dual CFT. The correlation function of EM with PMR tensors turns out to be zero which is expected according to the conformal symmetry. The two-point function of EM is that of a transverse and traceless tensor, and the two-point function of PMR which is a traceless operator contains two distinct parts, one for a transverse-traceless tensor operator and another one for a vector field, both of which fulfill criteria of a CFT. We also discuss about the unitarity of the theory.