论文标题
高维球形包装和模块化引导程序
High-dimensional sphere packing and the modular bootstrap
论文作者
论文摘要
我们对具有当前代数$ u（1）^c \ times u（1）^c $的无旋转模块化自举的数值研究，或等效地，在$ 2C $尺寸的球体包装中绑定了线性编程。我们对有限$ c $的行为的详细图片比以前可用，并以$ c \ to \ infty $的形式推断出来。我们的外推表明，高维度的球体堆积密度边界的指数改善。此外，我们研究这些界限何时可能很紧。除了已知的情况外，$ C = 1/2 $，$ 4 $和$ 12 $以及猜想的情况$ C = 1 $，我们的计算通过将模块化自举与线性编程界相结合的球形代码来排除所有其他$ c <90 $的急剧界限。
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.
