{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Henry Cohn","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/cohn\/","title":"High-Dimensional Sphere Packing and the Modular Bootstrap - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"QC4EWwQVLy\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/high-dimensional-sphere-packing-and-the-modular-bootstrap\/\">High-Dimensional Sphere Packing and the Modular Bootstrap<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/high-dimensional-sphere-packing-and-the-modular-bootstrap\/embed\/#?secret=QC4EWwQVLy\" width=\"600\" height=\"338\" title=\"&#8220;High-Dimensional Sphere Packing and the Modular Bootstrap&#8221; &#8212; Microsoft Research\" data-secret=\"QC4EWwQVLy\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","description":"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 [&hellip;]"}