Universality of Sparse $d>2$ Conformal Field Theory at Large $N$

Abstract

We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two dimensions and must be satisfied by any conformal field theory dual to Einstein gravity. We construct and analyze symmetric product orbifold theories on ${\mathbb{T}}^d$ and show that they only realize the necessary phase structure and extended range of validity if the seed theory is assumed to have a universal vacuum energy.

arXiv comment32 pages + appendices

References in corpus (35)

• Holography from Conformal Field Theory
• The D1/D5 System And Singular CFT
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• The Analytic Bootstrap and AdS Superhorizon Locality
• Two-dimensional conformal field theory and the butterfly effect
• Convexity and Liberation at Large Spin
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Emergent Spacetime and Holographic CFTs
• Correlation functions for M^N/S_N orbifolds
• Holographic Calculations of Renyi Entropy
• Causality Constraints in Conformal Field Theory
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• A Universal Inequality for CFT and Quantum Gravity
• Entanglement Scrambling in 2d Conformal Field Theory
• Bounding the Space of Holographic CFTs with Chaos
• Diagrams for Symmetric Product Orbifolds
• Instanton Strings and HyperKaehler Geometry
• Black Hole Collapse in the 1/c Expansion
• Constraints on 2d CFT partition functions
• Characters and modular properties of permutation orbifolds
• AdS Field Theory from Conformal Field Theory
• Universal Bounds on Charged States in 2d CFT and 3d Gravity
• Eikonalization of Conformal Blocks
• Hawking from Catalan
• Phase transitions in symmetric orbifold CFTs and universality
• Permutation orbifolds and holography
• Bounds on Operator Dimensions in 2D Conformal Field Theories
• Bounds for State Degeneracies in 2D Conformal Field Theory
• Black holes and universality classes of critical points
• Emergent space-time and the supersymmetric index
• Elliptic Genera and 3d Gravity

Cited by in corpus (43)

• Holography at finite cutoff with a $T^2$ deformation
• Einstein gravity 3-point functions from conformal field theory
• A General Proof of the Quantum Null Energy Condition
• The Conformal Bootstrap at Finite Temperature
• Global symmetry, Euclidean gravity, and the black hole information problem
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Bootstrapping Non-Invertible Symmetries
• Entanglement in De Sitter Space
• Einstein gravity from ANEC correlators
• OPE statistics from higher-point crossing
• Modular invariance on $S^1\times S^3$ and circle fibrations
• Universal Asymptotics for High Energy CFT Data
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• Thermal Conformal Blocks
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• Spectrum of End of the World Branes in Holographic BCFTs
• Parity and the modular bootstrap
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• Black holes from CFT: Universality of correlators at large c
• Encoding beyond cosmological horizons in de Sitter JT gravity
• Permutation Orbifolds and Chaos
• The Stranger Things of Symmetric Product Orbifold CFTs
• Comments on a state-operator correspondence for the torus
• Probing the EVH limit of supersymmetric AdS black holes
• The Holographic Landscape of Symmetric Product Orbifolds
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Flat space gravity at finite cutoff
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
• Gravitational wave driving of a gapped holographic system
• Siegel Paramodular Forms and Sparseness in AdS${}_3$/CFT${}_2$
• Bounds on CFTs with $W_3$ algebras and AdS${}_3$ higher spin theories
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• Component twist method for higher twists in D1D5 CFT
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Sparseness bounds on local operators in holographic $CF{T}_d$
• Generalized Hot Attractors
• A symmetry principle for emergent spacetime