Hidden Relations of Central Charges and OPEs in Holographic CFT
arXiv:2108.05384 · doi:10.1007/JHEP11(2021)135
Abstract
It is known that the central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.
arXiv commentLatex, 1 figure, 31 pages, typos corrected, a reference added, a technique issue clarified, to appear in JHEP
References in corpus (43)
- Gauge Theory Correlators from Non-Critical String Theory
- Black Hole Entropy is Noether Charge
- The Holographic Weyl anomaly
- Towards a derivation of holographic entanglement entropy
- On Renormalization Group Flows in Four Dimensions
- Implications of Conformal Invariance in Field Theories for General Dimensions
- Holography from Conformal Field Theory
- Conformal collider physics: Energy and charge correlations
- Holographic c-theorems in arbitrary dimensions
- Twenty Years of the Weyl Anomaly
- Causality Constraints on Corrections to the Graviton Three-Point Coupling
- Spinning Conformal Correlators
- Seeing a c-theorem with holography
- Holographic GB gravity in arbitrary dimensions
- Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
- Black Holes in Quasi-topological Gravity
- A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
- Averaged Null Energy Condition from Causality
- Holographic studies of quasi-topological gravity
- Einsteinian cubic gravity
- On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence
- A Proof of the Conformal Collider Bounds
- Einstein gravity 3-point functions from conformal field theory
- Aspects of general higher-order gravities
- (Generalized) quasi-topological gravities at all orders
- Harmonic Analysis and Mean Field Theory
- Bounds for OPE coefficients on the Regge trajectory
- AdS Bulk Locality from Sharp CFT Bounds
- Shocks, Superconvergence, and a Stringy Equivalence Principle
- Beyond : Gravitational Couplings to Matter and the Stress Tensor OPE
- Holographic studies of Einsteinian cubic gravity
- All higher-curvature gravities as Generalized quasi-topological gravities
- Lovelock theory and the AdS/CFT correspondence
- Universality of squashed-sphere partition functions
- A Conformal Collider for Holographic CFTs
- Einstein gravity from ANEC correlators
- Notes on flat-space limit of AdS/CFT
- A Bound on Massive Higher Spin Particles
- Helicity basis for three-dimensional conformal field theory
- Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities
- Universal Structure of Covariant Holographic Two-Point Functions In Massless Higher-Order Gravities
- Holographic Studies of The Generic Massless Cubic Gravities
- Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities