{"id":181846,"date":"2009-08-28T00:00:00","date_gmt":"2009-10-31T09:07:49","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-rigorous-perspective-on-liouville-quantum-gravity-kpz\/"},"modified":"2025-06-05T12:19:58","modified_gmt":"2025-06-05T19:19:58","slug":"a-rigorous-perspective-on-liouville-quantum-gravity-kpz","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/a-rigorous-perspective-on-liouville-quantum-gravity-kpz\/","title":{"rendered":"A Rigorous Perspective on Liouville Quantum Gravity & KPZ"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Polyakov first understood in 1981 that the summation over random Riemannian metrics involved in transition amplitudes in gauge theory or string theory could be represented mathematically by the now celebrated Liouville theory of quantum gravity.  The quantum gravity measure is formally defined by d mu<sub>gamma<\/sub> = exp[gamma h(z)]dz, where dz is the 2D Euclidean measure; exp[gamma h(z)] is the random conformal factor of the Riemannian metric, with h an instance of the Gaussian free field (GFF) on a bounded domain; and gamma is a constant, 0  2 is also shown to be related to the quantum measure for gamma&#8217; = 4 \/ gamma.<\/p>\n<p>This is joint work with Scott Sheffield.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Polyakov first understood in 1981 that the summation over random Riemannian metrics involved in transition amplitudes in gauge theory or string theory could be represented mathematically by the now celebrated Liouville theory of quantum gravity. The quantum gravity measure is formally defined by d mugamma = exp[gamma h(z)]dz, where dz is the 2D Euclidean measure; [&hellip;]<\/p>\n","protected":false},"featured_media":194330,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":null,"footnotes":""},"research-area":[243138],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-181846","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/KGCXJwVoW4w","msr_secondary_video_url":"","msr_video_file":"http:\/\/0","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/181846","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/181846\/revisions"}],"predecessor-version":[{"id":1141410,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/181846\/revisions\/1141410"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/194330"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=181846"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=181846"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=181846"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=181846"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=181846"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=181846"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=181846"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=181846"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=181846"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=181846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}