High-dimensional sphere packing and the modular bootstrap

Nima  Afkhami-Jeddi; Henry Cohn; Thomas Hartmann; David de Laat; Amirhossein Tajdinic

doi:10.1007/JHEP12(2020)066

High-dimensional sphere packing and the modular bootstrap

Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartmann, David de Laat, Amirhossein Tajdinic

Discrete Mathematics and Optimization

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Abstract

We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U(1)^c× U(1)^c, or equivalently the linear programming bound for sphere packing in 2c dimensions. We give a more detailed picture of the behavior for finite c than was previously available, and we extrapolate as c → ∞. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimen- sions. Furthermore, we study when these bounds can be tight. Besides the known cases c = 1/2, 4, and 12 and the conjectured case c = 1, our calculations numerically rule out sharp bounds for all other c < 90, by combining the modular bootstrap with linear programming bounds for spherical codes.

Original language	English
Article number	66
Pages (from-to)	1-44
Number of pages	44
Journal	Journal of High Energy Physics
Volume	2020
Issue number	12
DOIs	https://doi.org/10.1007/JHEP12(2020)066
Publication status	Published - 2020

Keywords

Conformal Field Theory
Field Theories in Lower Dimensions

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10.1007/JHEP12(2020)066

Afkhami-Jeddi2020_Article_High-dimensionalSpherePackingAFinal published version, 1.29 MBLicence: CC BY

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PY - 2020

Y1 - 2020

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AB - We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U(1)c× U(1)c, or equivalently the linear programming bound for sphere packing in 2c dimensions. We give a more detailed picture of the behavior for finite c than was previously available, and we extrapolate as c → ∞. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimen- sions. Furthermore, we study when these bounds can be tight. Besides the known cases c = 1/2, 4, and 12 and the conjectured case c = 1, our calculations numerically rule out sharp bounds for all other c < 90, by combining the modular bootstrap with linear programming bounds for spherical codes.

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High-dimensional sphere packing and the modular bootstrap

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