Universal Spectrum of 2d Conformal Field Theory in the Large c Limit

Abstract

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit $T\to \infty$, and a universal spectrum in the Cardy regime, $\Delta \to \infty$. We show that a much stronger form of universality holds in theories with a large central charge $c$ and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $\Delta \ge c/6$. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal `enigma' saddlepoints in the thermodynamics of 3d gravity.

37 pages

References in corpus (3)

• Three-Dimensional Gravity Revisited
• Entanglement Entropy at Large Central Charge
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT

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• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Charged structure constants from modularity
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• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Holographic Description of 2D Conformal Block in Semi-classical Limit
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• Black holes from CFT: Universality of correlators at large c
• Modular Bootstrap Revisited
• The holographic map as a conditional expectation
• The Holographic Landscape of Symmetric Product Orbifolds
• The Most Irrational Rational Theories
• Entropy Counting from Schwarzschild/CFT and Soft Hair
• Corrections to holographic entanglement plateau
• The Schwarzian sector of higher spin CFTs
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• Non-chiral 2d CFT with integer energy levels
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• Worldline approach to semi-classical conformal blocks
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