Holographic RG flows from running couplings

Abstract

In this paper, we investigate the RG flow in the holographic setup and study new IR physics at the IR fixed point, when a relevant scalar operator deforms a two-dimensional conformal field theory (CFT). On the dual gravity side, the renormalization group (RG) flow from the UV to the IR CFT can be described by a scalar field rolling from an unstable to a stable equilibrium point. Specifically, to make the scale dependence of the RG flow more explicit, we study the running coupling constant obtained by solving the beta function. After considering a simple scalar potential, we study the change of the coupling constant and its effect on the ground state along the RG flow. We showed that the central charge monotonically decreases along the RG flow and its value at the IR fixed point is determined by the conformal dimension of the deformation operator and the coupling constant at the IR fixed point. We further investigate how changing the ground state influences the two-point function and conformal dimension of a local operator in the probe limit.