  We show that the path-integral of conformal field theories in $D$ dimensions
(CFT$_D$) can be constructed by solving for eigenstates of an RG operator
following from the Turaev-Viro formulation of a topological field theory in
$D+1$ dimensions (TQFT$_{D+1}$), explicitly realising the holographic sandwich
relation between a symmetric theory and a TQFT. Generically, exact eigenstates
corresponding to symmetric-TQFT$_D$ follow from Frobenius algebra in the
TQFT$_{D+1}$. For $D=2$, we constructed eigenstates that produce 2D rational
CFT path-integral exactly, which, curiously connects a continuous field
theoretic path-integral with the Turaev-Viro state sum. We also devise and
illustrate numerical methods for $D=2,3$ to search for CFT$_D$ as phase
transition points between symmetric TQFT$_D$. Finally since the RG operator is
in fact an exact analytic holographic tensor network, we compute
``bulk-boundary'' correlator and compare with the AdS/CFT dictionary at $D=2$.
Promisingly, they are numerically compatible given our accuracy, although
further works will be needed to explore the precise connection to the AdS/CFT
correspondence.
