{"id":3506,"date":"2026-04-15T14:19:56","date_gmt":"2026-04-15T05:19:56","guid":{"rendered":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/?post_type=seminar&#038;p=3506"},"modified":"2026-04-15T14:19:56","modified_gmt":"2026-04-15T05:19:56","slug":"noncritical-conformal-gravity-and-4d-liouville-theory","status":"publish","type":"seminar","link":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/","title":{"rendered":"Noncritical Conformal Gravity and 4D Liouville Theory"},"content":{"rendered":"<p>We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar degrees of freedom.<br \/>\nWe demonstrate that this mismatch is resolved by carefully introducing gauge-fixing and ghost terms via the BRST symmetry, which effectively adds the two scalar modes. Drawing lessons from two-dimensional quantum gravity and Liouville theory, we proceed to integrate the four-dimensional trace anomaly to derive a consistent Liouville action, which is given by a free-field action for the conformal mode with a consistent conformal anomaly. Finally we give the condition that the BRST transformation is anomaly free.<\/p>\n","protected":false},"featured_media":0,"template":"","tags":[],"seminar_category":[154],"acf":{"s_now_accepting":true,"s_date_order":"2026-04-23 13:30:00","s_date_end":"2026-04-23 14:30:00","s_date_text":"13:30 - 14:30","s_text":"\u592a\u7530\u4fe1\u7fa9\uff08\u5927\u962a\u516c\u7acb\u5927\uff09","s_place":"ES635","s_place_other":"","s_categoryother":"","s_poster":"","s_poster2":"","s_slide":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University\" \/>\n<meta property=\"og:description\" content=\"We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar degrees of freedom. We demonstrate that this mismatch is resolved by carefully introducing gauge-fixing and ghost terms via the BRST symmetry, which effectively adds the two scalar modes. Drawing lessons from two-dimensional quantum gravity and Liouville theory, we proceed to integrate the four-dimensional trace anomaly to derive &hellip;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/\" \/>\n<meta property=\"og:site_name\" content=\"KMI - Nagoya University\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/\",\"url\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/\",\"name\":\"Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University\",\"isPartOf\":{\"@id\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/#website\"},\"datePublished\":\"2026-04-15T05:19:56+00:00\",\"dateModified\":\"2026-04-15T05:19:56+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Seminars\",\"item\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Noncritical Conformal Gravity and 4D Liouville Theory\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/#website\",\"url\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/\",\"name\":\"KMI - Nagoya University\",\"description\":\"Nagoya University: Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI)\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/","og_locale":"en_US","og_type":"article","og_title":"Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University","og_description":"We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar degrees of freedom. We demonstrate that this mismatch is resolved by carefully introducing gauge-fixing and ghost terms via the BRST symmetry, which effectively adds the two scalar modes. Drawing lessons from two-dimensional quantum gravity and Liouville theory, we proceed to integrate the four-dimensional trace anomaly to derive &hellip;","og_url":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/","og_site_name":"KMI - Nagoya University","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/","url":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/","name":"Noncritical Conformal Gravity and 4D Liouville Theory - KMI - Nagoya University","isPartOf":{"@id":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/#website"},"datePublished":"2026-04-15T05:19:56+00:00","dateModified":"2026-04-15T05:19:56+00:00","breadcrumb":{"@id":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/3506\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/"},{"@type":"ListItem","position":2,"name":"Seminars","item":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/seminar\/"},{"@type":"ListItem","position":3,"name":"Noncritical Conformal Gravity and 4D Liouville Theory"}]},{"@type":"WebSite","@id":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/#website","url":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/","name":"KMI - Nagoya University","description":"Nagoya University: Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI)","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/seminar\/3506"}],"collection":[{"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/types\/seminar"}],"wp:attachment":[{"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/media?parent=3506"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/tags?post=3506"},{"taxonomy":"seminar_category","embeddable":true,"href":"https:\/\/www.kmi.nagoya-u.ac.jp\/eng\/wp-json\/wp\/v2\/seminar_category?post=3506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}