Scaling dimension of operators from the black hole interior

Abstract

We propose a method to constrain the scaling dimension of the operators of the strongly interacting systems (SIS) using the holographic setup. We demonstrate our method using the holographic superconductor theory. 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 request the vanishing of log divergent term as well as an indefinite conditionally convergent terms that can lead to any real number according to Riemann. As a result, one gets quantized values of the scaling dimension of the condensing 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.