Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities

Abstract

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an $a$-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and $a$-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

arXiv commentLatex, 31 pages, typos corrected, comments and references added

References in corpus (48)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• Towards a derivation of holographic entanglement entropy
• Gauss-Bonnet Black Holes in AdS Spaces
• On Renormalization Group Flows in Four Dimensions
• On the Holographic Renormalization Group
• Holographic c-theorems in arbitrary dimensions
• Twenty Years of the Weyl Anomaly
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics
• Seeing a c-theorem with holography
• Black Holes in Quasi-topological Gravity
• Black Holes in Higher-Derivative Gravity
• Holographic Gravitational Anomalies
• Diffeomorphisms and Holographic Anomalies
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• F-Theorem without Supersymmetry
• Holographic studies of quasi-topological gravity
• Einsteinian cubic gravity
• Spherically Symmetric Solutions in Higher-Derivative Gravity
• The Holographic Renormalization Group
• On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Generalized quasi-topological gravity
• Aspects of general higher-order gravities
• On Subleading Contributions to the AdS/CFT Trace Anomaly
• Black Holes in (Quartic) Quasitopological Gravity
• Static Solutions for 4th order gravity
• Quintic quasi-topological gravity
• Quintessential Quartic Quasi-topological Quartet
• Holography, a covariant c-function, and the geometry of the renormalization group
• All unitary cubic curvature gravities in D dimensions
• Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity
• Counterterms and dual holographic anomalies in CS gravity
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• Black Holes in Six-dimensional Conformal Gravity
• Chern-Simons Gravity and Holographic Anomalies
• Universal Features of Holographic Anomalies
• Exact coefficients for higher dimensional operators with sixteen supersymmetries
• Quartic Quasi-topological Gravity, Black Holes and Holography
• Soft theorems from anomalous symmetries
• Counterterms, critical gravity and holography
• C-Functions in Lovelock Gravity
• Simple recipe for holographic Weyl anomaly
• Holographic Trace Anomaly and Local Renormalization Group

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• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
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