  According to more recent AdS/CFT interpretation \cite{Karch:2015rpa}, in
which varying cosmological constant $\Lambda$ in the bulk corresponds to
varying the curvature radius governing the space on which the field theory
resides, we study the criticality of thermodynamic curvatures for thermal
boundary conformal field theories (CFT) that are dual to $d$-dimensional
charged anti-de Sitter (AdS) black holes, embedded in $D$-dimensional
M-theory/superstring inspired models having $AdS_{d}\times \mathbb{S}^{d+k}$
spacetime with $D=2d+k$. Analogous with criticality features acquired for
charged AdS black holes in the bulk \cite{HosseiniMansoori:2020jrx}, the
normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ of the
boundary CFT has critical exponents 2 and 1, respectively. In this respect, the
universal amplitude of $R_Nt^2$ is $\frac{1}{2}$ and $K_Nt$ is $-\frac{1}{2}$
when $t\rightarrow0^-$, whereas $R_Nt^2\approx \frac{1}{8}$ and
$K_Nt\approx\frac{1}{4}$ in the limit $t\rightarrow0^+$ in which $t=T/T_c-1$ is
the temperature parameter with the critical temperature, $T_{c}$.
Interestingly, these critical amplitudes are independent of the number of
thermal CFT dimensions and are remarkably similar to one given for higher
dimensional charged AdS black holes in the bulk.
