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Sphere Packing and Quantum Gravity

We establish a precise relation between the modular bootstrap, used to con- strain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra U(1)$^{c}$ maps exactly to the Cohn-Elkies linear programming bound on the sphere packing d...

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Detalles Bibliográficos
Autores principales: Hartman, Thomas, Mazáč, Dalimil, Rastelli, Leonardo
Lenguaje:eng
Publicado: 2019
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP12(2019)048
http://cds.cern.ch/record/2675864
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author Hartman, Thomas
Mazáč, Dalimil
Rastelli, Leonardo
author_facet Hartman, Thomas
Mazáč, Dalimil
Rastelli, Leonardo
author_sort Hartman, Thomas
collection CERN
description We establish a precise relation between the modular bootstrap, used to con- strain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra U(1)$^{c}$ maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in d = 2c dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For c = 4 and c = 12, these functionals exactly repro- duce the “magic functions” used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension $ {\Delta}_0\underset{\sim }{<}c/\mathrm{8.503.} $
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2019
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spelling cern-26758642023-10-04T06:54:09Zdoi:10.1007/JHEP12(2019)048http://cds.cern.ch/record/2675864engHartman, ThomasMazáč, DalimilRastelli, LeonardoSphere Packing and Quantum Gravitymath.NTMathematical Physics and Mathematicsmath.MGMathematical Physics and Mathematicshep-thParticle Physics - TheoryWe establish a precise relation between the modular bootstrap, used to con- strain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra U(1)$^{c}$ maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in d = 2c dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For c = 4 and c = 12, these functionals exactly repro- duce the “magic functions” used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension $ {\Delta}_0\underset{\sim }{<}c/\mathrm{8.503.} $We establish a precise relation between the modular bootstrap, used to constrain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra $U(1)^c$ maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in $d=2c$ dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For $c=4$ and $c=12$, these functionals exactly reproduce the "magic functions" used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension $\Delta_0 \lesssim c/8.503$.arXiv:1905.01319oai:cds.cern.ch:26758642019-05-03
spellingShingle math.NT
Mathematical Physics and Mathematics
math.MG
Mathematical Physics and Mathematics
hep-th
Particle Physics - Theory
Hartman, Thomas
Mazáč, Dalimil
Rastelli, Leonardo
Sphere Packing and Quantum Gravity
title Sphere Packing and Quantum Gravity
title_full Sphere Packing and Quantum Gravity
title_fullStr Sphere Packing and Quantum Gravity
title_full_unstemmed Sphere Packing and Quantum Gravity
title_short Sphere Packing and Quantum Gravity
title_sort sphere packing and quantum gravity
topic math.NT
Mathematical Physics and Mathematics
math.MG
Mathematical Physics and Mathematics
hep-th
Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP12(2019)048
http://cds.cern.ch/record/2675864
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AT mazacdalimil spherepackingandquantumgravity
AT rastellileonardo spherepackingandquantumgravity