High-dimensional sphere packing and the modular bootstrap

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

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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 languageEnglish
Article number66
Pages (from-to)1-44
Number of pages44
JournalJournal of High Energy Physics
Volume2020
Issue number12
DOIs
Publication statusPublished - 2020

Keywords

  • Conformal Field Theory
  • Field Theories in Lower Dimensions

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