Holographic Renormalization Group Structure in Higher-Derivative Gravity

Classical higher-derivative gravity is investigated in the context of theholographic renormalization group (RG). We parametrize the Euclidean time suchthat one step of time evolution in (d+1)-dimensional bulk gravity can bedirectly interpreted as that of block spin transformation of the d-dimensionalboundary field theory. This parametrization simplifies the analysis of theholographic RG structure in gravity systems, and conformal fixed points arealways described by AdS geometry. We find that higher-derivative gravitygenerically induces extra degrees of freedom which acquire huge mass aroundstable fixed points and thus are coupled to highly irrelevant operators at theboundary. In the particular case of pure R^2-gravity, we show that some regionof the coefficients of curvature-squared terms allows us to have two fixedpoints (one is multicritical) which are connected by a kink solution. Wefurther extend our analysis to Minkowski time to investigate a model ofexpanding universe described by the action with curvature-squared terms andpositive cosmological constant, and show that, in any dimensionality but four,one can have a classical solution which describes time evolution from a deSitter geometry to another de Sitter geometry, along which the Hubble parameterchanges drastically.Comment: 26 pages, 6 figures, typos correcte