Holographic Renormalization Group Structure in Higher-Derivative Gravity

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 masses 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 values of the coefficients of the 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 Lorentzian metric to investigate a model of expanding universe described by the action with curvature-squared terms and a positive cosmological constant. We show that, in any dimensionality but four, there is a classical solution that describes the time evolution from one de Sitter geometry to another de Sitter geometry, along which the Hubble parameter changes significantly.