Holographic OPE Coefficients from AdS Black Holes with Matters

Abstract

We study the OPE coefficients $c_{\Delta ,J}$ for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension ${\Delta }_L$ in an AdS black hole. We verify that the OPE coefficient $c_{d,0}=0$ for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer ${\Delta }_L$, although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients ${\gamma }_{\Delta ,J}$ of the $\log (z\bar{z})$ terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for ${\gamma }_{\Delta ,J}$. We then consider charged AdS black holes in gauged supergravity STU models in $D=5$ and $D=7$, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with ${\Delta }_L=d-2$. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient $c_{d-2,0}$. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how $c_{d,0}$ can be nonzero with exchanging scalar operators in these backgrounds.

arXiv commentLatex, 53 pages, a serious technique error regarding $c_{d,0}$ corrected, typos corrected, references added

References in corpus (57)

• Gauge Theory Correlators from Non-Critical String Theory
• The Holographic Weyl anomaly
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Holography from Conformal Field Theory
• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Conformal collider physics: Energy and charge correlations
• The Analytic Bootstrap and AdS Superhorizon Locality
• Convexity and Liberation at Large Spin
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Four Dimensional String/String/String Triality
• Non-Extreme Black Holes of Five Dimensional N=2 AdS Supergravity
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Black Holes in Quasi-topological Gravity
• Holography and the Weyl anomaly
• Holographic Calculations of Renyi Entropy
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Holographic studies of quasi-topological gravity
• Einsteinian cubic gravity
• Holographic Hydrodynamics with a Chemical Potential
• AdS Dyonic Black Hole and its Thermodynamics
• Four-dimensional black holes in Einsteinian cubic gravity
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Black holes in Einsteinian cubic gravity
• Instanton Cosmology and Domain Walls from M-theory and String Theory
• Exact Black Holes and Universality in the Backreaction of non-linear Sigma Models with a potential in (A)dS4
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Dyonic AdS black holes in maximal gauged supergravity
• Exact asymptotically flat charged hairy black holes with a dilaton potential
• Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Holographic studies of Einsteinian cubic gravity
• Scalar Hairy Black Holes in General Dimensions
• On attractor mechanism of $Ad{S}_4$ black holes
• Universality of squashed-sphere partition functions
• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• Einstein gravity from ANEC correlators
• Anatomy of Geodesic Witten Diagrams
• Scalar Charges in Asymptotic AdS Geometries
• Witten Diagrams for Torus Conformal Blocks
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• Generalised Smarr Formula and the Viscosity Bound for Einstein-Maxwell-Dilaton Black Holes
• Exact Black Hole Formation in Asymptotically (A)dS and Flat Spacetimes
• Spinning Geodesic Witten Diagrams
• Static and Dynamic Hairy Planar Black Holes
• Lectures on Conformal Field Theory
• Exact black hole formation in three dimensions
• Universal Structure of Covariant Holographic Two-Point Functions In Massless Higher-Order Gravities
• Holographic Studies of The Generic Massless Cubic Gravities
• Exact Collapse Solutions in D=4, N=4 Gauged Supergravity and Their Generalizations
• Exact formation of hairy planar black holes
• Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Single-rotation two-charge black holes in gauged supergravity
• Holographic Aspects of Quasi-topological Gravity

Cited by in corpus (20)

• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Probing Universalities in d>2 CFTs: from Black Holes to Shockwaves
• Thermalization in Large-N CFTs
• Heavy-light Bootstrap from Lorentzian Inversion Formula
• Thermal Stress Tensor Correlators, OPE and Holography
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• Lightcone Commutator and Stress-Tensor Exchange in $d>2$ CFTs
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• Near Lightcone Thermal Conformal Correlators and Holography
• An embedding formalism for CFTs in general states on curved backgrounds
• On Local and Integrated Stress-Tensor Commutators
• Multi-stress tensors and next-to-leading singularities in the Regge limit
• $d>2$ Stress-Tensor OPE near a Line
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Interior analysis, stretched technique and bubbling geometries
• Stress Tensor Sector of Conformal Correlators
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Notes on AdS-Schwarzschild eikonal phase