# Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities

## TL;DR

This paper extends the universal relation between holographic $a$, $c$ charges and the energy-momentum tensor two-point function coefficient from 4 to 6 dimensions using massless higher-order gravities, revealing new universal holographic properties.

## Contribution

It establishes the first equality relating $a$ and $c$ charges in six dimensions within the holographic framework, generalizing previous 4-dimensional results.

## Key findings

- Universal relation between $a$ and $c$ charges in $d=6$
- Proportionality of the energy-momentum tensor two-point function coefficient to $c$
- Identification of $c$ as a specific combination of type-B anomalies

## Abstract

Recent studies of holographic properties of massless higher-order gravities, whose linear spectrum contains only the (massless) graviton, yielded some universal relations in $d=4$ dimensions between the holographic $a$, $c$ charges and the overall coefficient factor ${\cal C}_T$ of the energy-momentum tensor two-point function, namely $c=\frac{1}{d-1} \ell\frac{\partial a}{\partial \ell}={\cal C}_T$, where $\ell$ is the AdS radius. The second equality was shown to be valid in all dimensions. In this paper, we establish the first equality in $d=6$ by examining these quantities from $D=7$ higher-order gravities. Consequently the overall coefficient of the two-point function of the energy-momentum tensor is proportional to this $c$ charge, generalizing the well-known $d=4$ result. We identify the relevant $c$ charge as the coefficient of a specific combination of the three type-B anomalies. Modulo total derivatives, this combination involves Riemann tensor at most linearly.