Holographic c-theorems and higher derivative gravity

Abstract

In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly under flows to the IR. We prove such a c-theorem for higher curvature Lovelock gravity, where the bulk equations of motion remain second order. We also explore f(R) gravity as a toy model where higher derivatives cannot be avoided. In this case, monoticity of the flow requires an additional condition related to the higher derivative nature of the theory. This is in contrast to the case of f(R) black hole entropy, where the second law follows from application of the full Einstein equations and the null energy condition.

15 pages, revtex, references added

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• On the RG running of the entanglement entropy of a circle
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• New Massive Gravity and AdS_4 counterterms
• Holographic phase space: $c$-functions and black holes as renormalization group flows
• On c-theorems in arbitrary dimensions
• Entropy functionals and c-theorems from the second law
• Three Dimensional Modified Gravities as Holographic Limits of Lancsoz-Lovelock Theories
• A holographic c-theorem for higher derivative gravity
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
• Does anomalous violation of null energy condition invalidate holographic c-theorem?
• RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity
• The generalized holographic $c$-function for regular AdS black holes
• $c$-functions in Higher-derivative Flows Across Dimensions
• Holographic Aspects of a Higher Curvature Massive Gravity
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Extended First Law for Entanglement Entropy in Lovelock Gravity