Holographic Three-Point Functions from Higher Curvature Gravities in Arbitrary Dimensions

We calculate the holographic three-point function parameters $\mathcal{A}$, $\mathcal{B}$, $\mathcal{C}$ in general $d⩾4$ dimensions from higher curvature gravities up to and including the quartic order. The result is valid both for massless and perturbative higher curvature gravities. It is known that in four dimensional CFT the $a$-charge is a linear combination of $\mathcal{A}$, $\mathcal{B}$, $\mathcal{C}$, our result reproduces this but also shows that a similar relation does not exist for general $d>4$. We then compute the Weyl anomaly in $d=6$ and found all the three $c$-charges are linear combinations of $\mathcal{A}$, $\mathcal{B}$, $\mathcal{C}$, which is consistent with that the $a$-charge is not. We also find the previously conjectured relation between $t_2$, $t_4$, $h^{\mathrm{\prime }\mathrm{\prime }}$ does not hold in general massless gravities, but holds for quasi-topological ones, and we obtain the missing coefficient.