A holographic c-theorem for higher derivative gravity

2011/08/25 by James T. Liu, Liu, James T., Zhichen Zhao +1 · 14 citations
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Charge (physics) #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Energy condition #FOS: Physical sciences #General relativity #Geometry #Gravitation #High Energy Physics - Theory (hep-th) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Null (SQL) #Physics #Quantum mechanics #Ricci curvature #Riemann curvature tensor #Riemann hypothesis #Scalar (mathematics) #Scalar curvature #Sign (mathematics) #hep-th

paper · pdf · doi:10.48550/arxiv.1108.5179

published in arXiv (Cornell University) (Cornell University) · 12 pages

arxiv created 2011/08/25 · openalex publication_date 2011/08/25 · arxiv updated 2011/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a holographic c-theorem for the a central charge in AdS/CFT where the bulk is described by a gravitational action built out of an arbitrary function f(R^ab_cd) of the Riemann tensor coupled to bulk matter. This theorem holds provided a generalized null energy condition involving both matter and higher curvature gravitational interactions is satisfied. As an example, we consider the case of a curvature-squared action, and find that generically the generalized null energy condition involves not just the bulk matter, but also the sign of R" where a prime denotes a radial derivative and where R is the bulk scalar curvature.

Citations

• New Results on the "a-theorem" in Four Dimensional Supersymmetric Field Theory
• Is there a c-theorem in four dimensions?
• Evidence for the strongest version of the 4d a-theorem via a-maximization along RG flows
• Analogs of the c-theorem for four-dimensional renormalisable field theories
• Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes
• Holographic c-theorems in arbitrary dimensions
• Some properties of the Noether charge and a proposal for dynamical black hole entropy
• Novel local CFT and exact results on perturbations of N = 4 super Yang Mills from AdS dynamics

Related

• Holography and the C-Theorem
• Holographic c-theorems in arbitrary dimensions
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• Holographic Reconstruction of Gravitational Perturbations in AdS/CFT and Implications for Celestial Conformal Field Theory
• Holographic c-Function