Holographic three-point functions from higher curvature gravities in arbitrary dimensions

The three-point function of the energy-momentum tensor in a conformal field theory is completely determined by three parameters, called $A$, $B$, $C$. We carry out a holographic calculation of these three parameters in general $d\ge 4$ 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 conformal field theory (CFT) the $a$-charge is a linear combination of $A$, $B$, $C$, 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 $A$, $B$, $C$, which is consistent with that the $a$-charge is not. We also find the previously conjectured relation between $t_2$, $t_4$, $h^{\prime \prime }$ does not hold in general massless gravities.