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Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ

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arxiv 1702.00423 v1 pith:F4LIQLDM submitted 2017-02-01 hep-th

Scott Collier , Petr Kravchuk , Ying-Hsuan Lin , Xi Yin This is my paper · ORCID
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keywords spectralfunctionliouvilledensitylargemodularprimariesresults
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We introduce spectral functions that capture the distribution of OPE coefficients and density of states in two-dimensional conformal field theories, and show that nontrivial upper and lower bounds on the spectral function can be obtained from semidefinite programming. We find substantial numerical evidence indicating that OPEs involving only scalar Virasoro primaries in a c>1 CFT are necessarily governed by the structure constants of Liouville theory. Combining this with analytic results in modular bootstrap, we conjecture that Liouville theory is the unique unitary c>1 CFT whose primaries have bounded spins. We also use the spectral function method to study modular constraints on CFT spectra, and discuss some implications of our results on CFTs of large c and large gap, in particular, to what extent the BTZ spectral density is universal.

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Cited by 3 Pith papers

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  1. A microscopic realization of dS$_3$

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    Pure dS3 quantum gravity is claimed to be dual to the complex Liouville string's matrix integral, with integrated cosmological correlators equal to resolvent correlators and de Sitter entropy equal to 2 log of the eig...

  2. Bootstrapping $\mathcal{N} = 4$ sYM correlators using Integrability and Localization

    hep-th 2024-11 conditional novelty 7.0 of 10

    Two-sided bounds on the Konishi OPE coefficient in planar N=4 sYM are derived at finite 't Hooft coupling by adding localization constraints to an integrability-based dispersive bootstrap.

  3. Entanglement Entropy after Double-Excitation as Interaction Measure

    hep-th 2019-08 conditional novelty 6.0 of 10

    For double local operator excitations in pure 2D CFTs, the late-time entanglement entropy equals the sum of two single-quench results plus a negative c/6 log((l_B - l_A)/(t - l_A)) interaction term.

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