Phys. Rev. D 99, 126003 (2019)        arXiv link

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

H. Lü^1,* and Rui Wen^2,†

¹Center for Joint Quantum Studies, School of Science Tianjin University, Tianjin 300350, China

²School of Physics, University of Science and Technology of China, Hefei 230026, China

*mrhonglu@gmail.com

†wenrui1024@outlook.com

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.