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High-dimensional sphere packing and the modular bootstrap

Journal Article (2020)
Author(s)

Nima Afkhami-Jeddi (University of Chicago)

Henry Cohn (Microsoft Research New England)

Thomas Hartmann (Cornell University)

D. de Laat (TU Delft - Discrete Mathematics and Optimization)

Amirhossein Tajdinic (Cornell University)

Research Group
Discrete Mathematics and Optimization
Copyright
© 2020 Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartmann, D. de Laat, Amirhossein Tajdinic
DOI related publication
https://doi.org/10.1007/JHEP12(2020)066
More Info
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Publication Year
2020
Language
English
Copyright
© 2020 Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartmann, D. de Laat, Amirhossein Tajdinic
Research Group
Discrete Mathematics and Optimization
Issue number
12
Volume number
2020
Pages (from-to)
1-44
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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.