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High-dimensional sphere packing and the modular bootstrap

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arxiv 2006.02560 v2 pith:DVGE2TOP submitted 2020-06-03 hep-th math.MG

High-dimensional sphere packing and the modular bootstrap

Nima Afkhami-Jeddi , Henry Cohn , Thomas Hartman , David de Laat , Amirhossein Tajdini This is my paper
classification hep-th math.MG
keywords boundsbootstrapmodularpackingspheredimensionslinearprogramming
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra $U(1)^c \times U(1)^c$, 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 $c \to \infty$. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimensions. 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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Neural Spectral Bias and Conformal Correlators II: Modular and Annulus Bootstrap

    hep-th 2026-07 conditional novelty 6.0

    Lightweight neural nets with spectral bias reconstruct full 2d CFT torus and annulus partition functions from crossing, a gap, and a single interior anchor to sub-percent accuracy on known theories.

  2. A dual linear programming bound for sphere packing in dimension 36

    math.MG 2026-07 conditional novelty 6.0

    An exact dual Cohn–Elkies certificate in dimension 36 proves the LP bound exceeds the Kschischang–Pasupathy packing density by ≥32.91, so that packing cannot be certified optimal by any Cohn–Elkies auxiliary function.

  3. A dual linear programming bound for sphere packing in dimension 36

    math.MG 2026-07 accept novelty 6.0

    In dimension 36, a modular-form certificate proves the Cohn–Elkies LP bound exceeds the density of the best known packing by at least a factor of 32.9.

  4. Upgrading Extremal Flows in the Space of Derivatives

    hep-th 2026-04 unverdicted novelty 6.0

    A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.