| Title: |
High-dimensional sphere packing and the modular bootstrap |
| Authors: |
Afkhami-Jeddi, Nima; Cohn, Henry; Hartman, Thomas; de Laat, David; Tajdini, Amirhossein |
| Source: |
J. High Energ. Phys. 12 (2020) 66 |
| Publication Year: |
2020 |
| Collection: |
Mathematics; High Energy Physics - Theory |
| Subject Terms: |
High Energy Physics - Theory; Mathematics - Metric Geometry |
| Description: |
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 |
| Document Type: |
Working Paper |
| DOI: |
10.1007/JHEP12(2020)066 |
| Access URL: |
http://arxiv.org/abs/2006.02560 |
| Accession Number: |
edsarx.2006.02560 |
| Database: |
arXiv |