IR physics from the holographic RG flow

Abstract

We use the holographic method to investigate an RG flow and IR physics of a two-dimensional conformal field theory (CFT) deformed by a relevant scalar operator. On the dual gravity side, a renormalization group (RG) flow from a UV to IR CFT can be described by rolling a scalar field from an unstable to a stable equilibrium point. After considering a simple scalar potential allowing several local equilibrium points, we study the change of a coupling constant and ground state from the momentum-space and real-space RG flow viewpoints. For the real-space RG flow, we calculate the entanglement entropy as a function of a coupling constant and then explicitly show that the entanglement entropy diverges logarithmically at fixed points due to the restoration of conformal symmetry. We further study how the change of a ground state affects the two-point function and conformal dimension of a local operator numerically and analytically in the probe limit.