  In this paper, we study the holographic descriptions of the conformal block
of heavy operators in two-dimensional large c conformal field theory. We
consider the case that the operators are pairwise inserted such that the
distance between the operators in a pair is much smaller than the others. In
this case, each pair of heavy operators creates a conical defect in the bulk.
We propose that the conformal block is dual to the on-shell action of three
dimensional geometry with conical defects in the semi-classical limit. We show
that the variation of the on-shell action with respect to the conical angle is
equal to the length of the corresponding conical defect. We derive this
differential relation on the conformal block in the field theory by introducing
two extra light operators as both the probe and the perturbation. Our study
also suggests that the area law of the holographic Renyi entropy must holds for
a large class of states generated by a finite number of heavy operators
insertion.
