Universal Lowest-Twist in CFTs from Holography

Abstract

We probe the conformal block structure of a scalar four-point function in $d\ge 2$ conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge $C_T$. Neither supersymmetry nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limit in this paper, we include some preliminary analysis of the spherical black hole case in an appendix.

arXiv comment63 pp; v2: comments on additional bulk interactions added

References in corpus (45)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Eternal Black Holes in AdS
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Holography from Conformal Field Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Two-dimensional conformal field theory and the butterfly effect
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• The Black Hole Singularity in AdS/CFT
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Black Holes in Quasi-topological Gravity
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Unitarity and the Holographic S-Matrix
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Holographic studies of quasi-topological gravity
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Analyticity and the Holographic S-Matrix
• Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
• Black Holes, Shock Waves, and Causality in the AdS/CFT Correspondence
• Boundary Conformal Field Theory and a Boundary Central Charge
• Black Hole Collapse in the 1/c Expansion
• Aspects of general higher-order gravities
• AdS Field Theory from Conformal Field Theory
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Hawking from Catalan
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Higher-point conformal blocks and entanglement entropy in heavy states
• An Exact Operator That Knows Its Location
• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• Stress Tensors from Trace Anomalies in Conformal Field Theories
• Phases of scrambling in eigenstates
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Spinning Geodesic Witten Diagrams
• Superconformal Models for Graphene and Boundary Central Charges
• Holographic Entanglement Entropy For a Large Class of States in 2D CFT
• Weyl Anomaly Induced Stress Tensors in General Manifolds
• The AdS${}_3$ Propagator and the Fate of Locality

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