Holographic Renormalization Group Structure in Higher-Derivative Gravity

TL;DR

This paper explores the holographic renormalization group in higher-derivative gravity, revealing how additional degrees of freedom behave near fixed points and identifying conditions for multiple fixed points and cosmological solutions.

Contribution

It introduces a simplified parametrization of holographic RG flow in higher-derivative gravity and analyzes fixed points, including multicritical points and cosmological solutions with curvature-squared terms.

Findings

Higher-derivative gravity induces massive extra degrees of freedom.

Existence of multiple fixed points connected by kink solutions in R^2 gravity.

Time evolution solutions from one de Sitter universe to another in higher dimensions.

Abstract

Classical higher-derivative gravity is investigated in the context of the holographic renormalization group (RG). We parametrize the Euclidean time such that one step of time evolution in (d+1)-dimensional bulk gravity can be directly interpreted as that of block spin transformation of the d-dimensional boundary field theory. This parametrization simplifies the analysis of the holographic RG structure in gravity systems, and conformal fixed points are always described by AdS geometry. We find that higher-derivative gravity generically induces extra degrees of freedom which acquire huge mass around stable fixed points and thus are coupled to highly irrelevant operators at the boundary. In the particular case of pure R^2-gravity, we show that some region of the coefficients of curvature-squared terms allows us to have two fixed points (one is multicritical) which are connected by a kink solution. We further extend our analysis to Minkowski time to investigate a model of expanding universe described by the action with curvature-squared terms and positive cosmological constant, and show that, in any dimensionality but four, one can have a classical solution which describes time evolution from a de Sitter geometry to another de Sitter geometry, along which the Hubble parameter changes drastically.