Universal spectrum of 2d conformal field theory in the large c limit

By Thomas Hartman, Christoph A. Keller, Bogdan Stoica. 2014

399 citations recorded by the source corpus.

A bstractTwo-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. 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 Δ≥c6$$ \Delta \ge \frac{c}{6} $$. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba4df1a8107339c86fcaf95d8154a8c592a00db8

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Citations in the corpus

Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, methodology): “3) is precisely the transformation from the microcanonical to the canonical ensemble in sparse CFTs [6].”
Holography at finite cutoff with a T2 deformation (2018, methodology): “f center symmetry breaking [43], this formula has an extended range of validity [44], holding down to ener25 gies −(d − 1)Evac. (For d = 2 this extended range is equivalent to a sparse light spectrum [45]; for the connection to a sparse light spectrum in d > 2 see [42,43].) This means that the en”
TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, positive): “In some special cases we can even match the O(1) coefficient, giving a microscopic derivation of the Bekenstein-Hawking entropy formula [34, 35, 36].”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “those with c 1 and a sparse density of states with EL c, the above density of states formula is supposed [138] to hold also for EL = O(c), in which case it may be argued that (34) holds out to times t = O(cL).”
Entanglement of local operators in large-N conformal field theories (2014, positive): “8 If we focus on the modes b corresponding to the large conformal dimension ∆b ≫ c, we can apply the Cardy’s formula [31] to estimate the number of primaries in the large c limit.”
Black hole collapse in the 1/c expansion (2016, background): “This is exactly what was proved for the torus partition function in [10], and we will assume the same applies to the correlators considered here.”
Bounding the space of holographic CFTs with chaos (2016, background): “We note that all Sym CFTs are sparse in the precise sense of [63].”
Causality constraints in conformal field theory (2015, background): “, modular invariance) of the genus one partition function leads to a CFT derivation of black hole entropy at high temperatures [40], and adding to this derivation the assumption of a sparse spectrum extends the match to all temperatures [41].”
Holographic Quantum Matter (2016, background): “Beyond the holographic approach discussed here, the development of purely quantum field theoretic methods exploiting the existence of an operator gap has recently been initiated [237; 262; 264; 331].”
A cardy formula for three-point coefficients or how the black hole got its spots (2016, methodology): “rticular, while the average three-point coecient vanishes exponentially as E!1, individual three-point coecients might be large. Many of the more precise generalizations of Cardy’s formula, such as [13, 14, 15], rely on the fact that in Cardy’s formula the partition function is a sum of positive den”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, neutral): “[43–46].”