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.
Highlights
The Wilsonian approach in renormalization of quantum field theories (QFTs) [1,2], leads to the concept of the renormalization group (RG) by integrating out the high energy degrees of freedom
The RG flow of the QFT on the boundary is related to the various geometries of the bulk gravity, and a holographic dimension plays the role of the RG scale in the dual QFT
The RG flow between two fixed points of the QFT is supposed to be given by a domain wall solution on the gravity side which connects two AdS geometries
Summary
The Wilsonian approach in renormalization of quantum field theories (QFTs) [1,2], leads to the concept of the renormalization group (RG) by integrating out the high energy degrees of freedom. It is important when the quantum field theory is in the strong coupling regime in which the perturbation theory does not work Because of this correspondence, the RG flow of the QFT on the boundary is related to the various geometries of the bulk gravity, and a holographic dimension plays the role of the RG scale in the dual QFT. The holographic RG flow of the general quadratic curvature (GQC) gravity in a simple toy model has been studied in [39].1 It shows the existence of the a-theorem for even-dimensional theories by finding the Wess-Zumino action, which originates from the spontaneous breaking of the conformal symmetry, by using a radial cutoff near the. The first choice to study the higher curvature corrections is the GB gravity, in which the order of derivatives of the equations of motion is the same as the EH action.
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