High-dimensional sphere packing and the modular bootstrap

Journal article (2020)

Authors

Nima Afkhami-Jeddi University of Chicago
Henry Cohn Microsoft Research New England
Thomas Hartmann Cornell University
D. de Laat Discrete Mathematics and Optimization - EEMCS
Amirhossein Tajdinic Cornell University
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2020 Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartmann, D. de Laat, Amirhossein Tajdinic
DOI
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https://doi.org/10.1007/JHEP12(2020)066
Conformal Field Theory Field Theories in Lower Dimensions
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Published Date

2020

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

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.