Scaling Dimension of the Operators from the Black hole inside

We propose a method to constrain the scaling dimension of the operators of the strongly interacting systems (SIS) using the holographic setup where the (d+1)-dimensional black hole is used to describe the d-dimensional SIS. We demonstrate the method in the holographic superconductor theory where the operator is a scalar. The idea is to consider the inside as well as the outside of the AdS black hole in which the gap equations has higher order singularities. Then the equivalence principle requests the solution be smoothly connected at the horizon, which turns out to give a quantized values of the scaling dimension of the condensed operator. This is a pleasant surprise because so far one gets the constraints on the scaling dimension only by a hard analysis with bootstrap ansatz.