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Home > Physical Review D (APS) > Holographic <math><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>)</mo></math> charges and their universal relation in <math><mi>d</mi><mo>=</mo><mn>6</mn></math> 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)**
**Published by: **APS

**DOI: **10.1103/PhysRevD.99.126003

**License: **CC-BY-4.0