TY - JOUR
T1 - High-dimensional sphere packing and the modular bootstrap
AU - Afkhami-Jeddi, Nima
AU - Cohn, Henry
AU - Hartmann, Thomas
AU - de Laat, David
AU - Tajdinic, Amirhossein
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Conformal Field Theory
KW - Field Theories in Lower Dimensions
UR - http://www.scopus.com/inward/record.url?scp=85097418325&partnerID=8YFLogxK
U2 - 10.1007/JHEP12(2020)066
DO - 10.1007/JHEP12(2020)066
M3 - Article
AN - SCOPUS:85097418325
SN - 1029-8479
VL - 2020
SP - 1
EP - 44
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 12
M1 - 66
ER -