Higher order curvature corrections and holographic renormalization group flow

TL;DR

This paper explores how higher-order curvature corrections influence holographic RG flows, critical points, and the existence of c-functions, using the superpotential approach in Einstein-Hilbert gravity with scalar matter.

Contribution

It extends the holographic RG flow analysis to include higher-order curvature corrections and examines the impact on critical points and c-function behavior.

Findings

Existence of bounce solutions in RG flow.

Superpotential bounds differ from Einstein-Hilbert gravity.

RG flow behavior is governed by singular curves.

Abstract

We study the holographic renormalization group (RG) flow in the presence of higher-order curvature corrections to the $(d+1)$-dimensional Einstein-Hilbert (EH) action for an arbitrary interacting scalar matter field by using the superpotential approach. We find the critical points of the RG flow near the local minima and maxima of the potential and show the existence of the bounce solutions. In contrast to the EH gravity, regarding the values of couplings of the bulk theory, superpotential may have both upper and lower bounds. Moreover, the behavior of the RG flow controls by singular curves. This study may shed some light on how a c-function can exist in the presence of these corrections.