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.
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Afkhami-Jeddi, N., Cohn, H., Hartman, T. et al. High-dimensional sphere packing and the modular bootstrap. J. High Energ. Phys. 2020, 66 (2020). https://doi.org/10.1007/JHEP12(2020)066
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DOI: https://doi.org/10.1007/JHEP12(2020)066