c-theorem of the entanglement entropy

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 analytically 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.