# Holographic $\left(a,c\right)$ charges and their universal relation in $d=6$ from massless higher-order gravities

Lü, H. (Center for Joint Quantum Studies, School of Science Tianjin University, Tianjin 300350, China) ; Wen, Rui (School of Physics, University of Science and Technology of China, Hefei 230026, China)

12 June 2019

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 $a$ and $c$ charges and the overall coefficient factor ${C}_{T}$ of the energy-momentum tensor two-point function, namely, $c=\frac{1}{d-1}\ell \frac{\partial a}{\partial \ell }={C}_{T}$, where $\ell$ is the anti–de Sitter 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 the Riemann tensor at most linearly.

Published in: Physical Review D 99 (2019)