{"work":{"id":"a9b529fb-6c73-4538-bd9a-a78fdfeee5fc","openalex_id":null,"doi":null,"arxiv_id":"2211.16045","raw_key":null,"title":"Fun with replicas: tripartitions in tensor networks and gravity","authors":null,"authors_text":"G","year":2022,"venue":"hep-th","abstract":"We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and is bounded from above by $\\log d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with $A$, $B$, and $C$. We argue that for holographic states with a fixed spatial geometry, $G(A:B:C)$ is similarly computed by the minimal area tripartition. For general holographic states, $G(A:B:C)$ is determined by the minimal area tripartition in a backreacted geometry, but a smoothed version is equal to the minimal tripartition in an unbackreacted geometry at leading order. We briefly discuss a natural family of quantities $G_n(A:B:C)$ for integer $n \\geq 2$ that generalize $G=G_2$. In holography, the computation of $G_n(A:B:C)$ for $n>2$ spontaneously breaks part of a $\\mathbb{Z}_n \\times \\mathbb{Z}_n$ replica symmetry. This prevents any naive application of the Lewkowycz-Maldacena trick in a hypothetical analytic continuation to $n=1$.","external_url":"https://arxiv.org/abs/2211.16045","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-08T18:25:25.747869+00:00","pith_arxiv_id":"2211.16045","created_at":"2026-05-11T09:26:03.122589+00:00","updated_at":"2026-07-08T18:25:25.747869+00:00","title_quality_ok":true,"display_title":"Penington, M","render_title":"Penington, M"},"hub":{"state":{"work_id":"a9b529fb-6c73-4538-bd9a-a78fdfeee5fc","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":16,"external_cited_by_count":null,"distinct_field_count":3,"first_pith_cited_at":"2025-08-30T19:10:25+00:00","last_pith_cited_at":"2026-07-07T09:26:44+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":"2026-08-20T00:30:07.917367+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":4}],"polarity_counts":[{"context_polarity":"background","n":4}],"runs":{},"summary":{},"graph":{},"authors":[]}}