{"id":84,"date":"2015-03-31T01:37:42","date_gmt":"2015-03-31T01:37:42","guid":{"rendered":"https:\/\/stikonas.eu\/wordpress\/?p=84"},"modified":"2015-08-06T21:37:32","modified_gmt":"2015-08-06T21:37:32","slug":"scrambling-time-from-local-perturbations-of-the-eternal-btz-black-hole","status":"publish","type":"post","link":"https:\/\/stikonas.eu\/wordpress\/2015\/03\/31\/scrambling-time-from-local-perturbations-of-the-eternal-btz-black-hole\/","title":{"rendered":"Scrambling time from local perturbations of the eternal BTZ black hole"},"content":{"rendered":"<p><a href=\"http:\/\/arxiv.org\/find\/hep-th\/1\/au:+Caputa_P\/0\/1\/0\/all\/0\/1\">Pawe\u0142 Caputa<\/a>, <a href=\"http:\/\/arxiv.org\/find\/hep-th\/1\/au:+Simon_J\/0\/1\/0\/all\/0\/1\">Joan Sim\u00f3n<\/a>, <a href=\"http:\/\/arxiv.org\/find\/hep-th\/1\/au:+Stikonas_A\/0\/1\/0\/all\/0\/1\">Andrius \u0160tikonas<\/a>, <a href=\"http:\/\/arxiv.org\/find\/hep-th\/1\/au:+Takayanagi_T\/0\/1\/0\/all\/0\/1\">Tadashi Takayanagi<\/a>, <a href=\"http:\/\/arxiv.org\/find\/hep-th\/1\/au:+Watanabe_K\/0\/1\/0\/all\/0\/1\">Kento Watanabe<\/a><\/p>\n<p>We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time <em>t<sub>\u03c9<\/sub><\/em> in the large <em>c<\/em>\u00a0limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time\u00a0<em>t<sub>\u03c9<\/sub><\/em>. In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.<\/p>\n<p><a href=\"http:\/\/download.springer.com\/static\/pdf\/536\/art%253A10.1007%252FJHEP08%25282015%2529011.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2FJHEP08%282015%29011&amp;token2=exp=1438898154~acl=%2Fstatic%2Fpdf%2F536%2Fart%25253A10.1007%25252FJHEP08%2525282015%252529011.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252FJHEP08%25282015%2529011*~hmac=502f828ba8bb1ae6741b0f0c6b3ea75c5f1f3591f3f7d2cbf63f1bc69df9aea0\">Published in JHEP<\/a>.<\/p>\n<p><a href=\"https:\/\/cgit.stikonas.eu\/scrambling.git\/\">Some source code<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pawe\u0142 Caputa, Joan Sim\u00f3n, Andrius \u0160tikonas, Tadashi Takayanagi, Kento Watanabe We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time t\u03c9 in the large c\u00a0limit. We determine the time scale, called the &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[18],"tags":[23,27,24,22,26,20,19,29,32,28,21,34,33,30,31,25],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-research","tag-ads","tag-adscft","tag-anti-de-sitter","tag-btz","tag-cft","tag-entanglement","tag-entropy","tag-field-theory","tag-gaugegravity-duality","tag-gravity","tag-information","tag-local-excitation","tag-mutual-information","tag-scrambling","tag-scrambling-time","tag-thermofield-double"],"_links":{"self":[{"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/posts\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/comments?post=84"}],"version-history":[{"count":0,"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/posts\/84\/revisions"}],"wp:attachment":[{"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/categories?post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stikonas.eu\/wordpress\/wp-json\/wp\/v2\/tags?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}