c-theorem of the entanglement entropy

TL;DR

This paper holographically studies the RG flow in 2D CFTs deformed by relevant operators, demonstrating a monotonic decrease of the entanglement entropy c-function from UV to IR, consistent with the c-theorem.

Contribution

It provides an analytical and numerical analysis of the entanglement entropy c-function along holographic RG flows, confirming its monotonic behavior and connection to central charges.

Findings

The c-function decreases monotonically along the RG flow.

The c-function matches the expected UV and IR central charges.

The flow interpolates between two AdS geometries without phase transitions.

Abstract

We holographically investigate the renormalization group flow in a two-dimensional conformal field theory deformed by a relevant operator. If the relevant operator allows another fixed point, the UV conformal field theory smoothly flows to a new IR conformal field theory. From the holographic point of view, such a renormalization group flow can be realized as a dual geometry interpolating two different AdS boundaries. On this interpolating geometry, we investigate how the c-function of the entanglement entropy behaves along the RG flow analyt- ically and numerically, which reproduces the expected central charges of UV and IR. We also show that the c-function monotonically decreases from UV to IR without any phase transition.