{"id":669963,"date":"2020-06-26T10:03:55","date_gmt":"2020-06-26T17:03:55","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=669963"},"modified":"2020-06-26T10:03:55","modified_gmt":"2020-06-26T17:03:55","slug":"high-dimensional-sphere-packing-and-the-modular-bootstrap","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/high-dimensional-sphere-packing-and-the-modular-bootstrap\/","title":{"rendered":"High-Dimensional Sphere Packing and the Modular Bootstrap"},"content":{"rendered":"

We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U<\/em>(1)c<\/em> \u00d7 U<\/em>(1)c<\/em>, or equivalently the linear programming bound for sphere packing in 2c<\/em> dimensions. We give a more detailed picture of the behavior for finite c than was previously available, and we extrapolate as c<\/em> \u2192 \u221e. 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<\/em> = 1\/2, 4, and 12 and the conjectured case c<\/em> = 1, our calculations numerically rule out sharp bounds for all other c<\/em> < 90, by combining the modular bootstrap with linear programming bounds for spherical codes.<\/p>\n","protected":false},"excerpt":{"rendered":"

We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U(1)c \u00d7 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 \u2192 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Afkhami-Jeddi","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Henry Cohn","user_id":31460,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Henry Cohn"},{"type":"text","value":"Thomas Hartman","user_id":0,"rest_url":false},{"type":"text","value":"David de Laat","user_id":0,"rest_url":false},{"type":"text","value":"Amirhossein 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