IR physics from the holographic RG flow

TL;DR

This paper uses holographic duality to analyze the RG flow and IR physics of a 2D CFT deformed by a relevant scalar operator, revealing how entanglement entropy and operator dimensions evolve along the flow.

Contribution

It provides a detailed holographic study of RG flows with multiple equilibrium points, including entanglement entropy behavior and operator dimension changes.

Findings

Entanglement entropy diverges logarithmically at fixed points.

Ground state changes affect two-point functions and conformal dimensions.

Holographic RG flow describes scalar field evolution from unstable to stable points.

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.