{"work":{"id":"24b0e278-57a7-4cc4-b793-e93653b59371","openalex_id":null,"doi":null,"arxiv_id":"hep-th/9912012","raw_key":null,"title":"On the Holographic Renormalization Group","authors":null,"authors_text":"J","year":1999,"venue":"hep-th","abstract":"We propose a direct correspondence between the classical evolution equations of 5-d supergravity and the renormalization group (RG) equations of the dual 4-d large $N$ gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action $S$, that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of $S$ with the quantum effective action of the gauge theory. In addition we find interesting new relations between the beta-functions and the counterterms that affect the 4-d cosmological and Newton constant.","external_url":"https://arxiv.org/abs/hep-th/9912012","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-01T11:35:43.321869+00:00","pith_arxiv_id":"hep-th/9912012","created_at":"2026-05-12T05:56:24.512427+00:00","updated_at":"2026-07-01T11:35:43.321869+00:00","title_quality_ok":false,"display_title":"On the Holographic Renormalization Group","render_title":"On the Holographic Renormalization Group"},"hub":{"state":{"work_id":"24b0e278-57a7-4cc4-b793-e93653b59371","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":13,"external_cited_by_count":null,"distinct_field_count":1,"first_pith_cited_at":"2021-05-31T04:01:54+00:00","last_pith_cited_at":"2026-06-30T16:07:36+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-03T13:14:23.931795+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":5}],"polarity_counts":[{"context_polarity":"background","n":4},{"context_polarity":"support","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}