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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...
Autores principales: | , , |
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Lenguaje: | eng |
Publicado: |
2019
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/JHEP12(2019)048 http://cds.cern.ch/record/2675864 |
_version_ | 1780962692454940672 |
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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.} $ |
id | cern-2675864 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2019 |
record_format | invenio |
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 |
work_keys_str_mv | AT hartmanthomas spherepackingandquantumgravity AT mazacdalimil spherepackingandquantumgravity AT rastellileonardo spherepackingandquantumgravity |