{"paper":{"title":"Conformal defects and Goldstone bosons in Anti-de Sitter space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Conformal defects in Anti-de Sitter space host a displacement operator whose dimension is fixed by residual symmetry, even when the boundary theory is non-local.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Elia de Sabbata, Lorenzo Bianchi, Marco Meineri","submitted_at":"2026-05-13T18:00:00Z","abstract_excerpt":"We study local quantum field theories in Anti-de Sitter (AdS) space, with boundary conditions that break some of the bulk isometries. Specifically, we focus on conformal defects and we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present. The existence of a displacement was conjectured in arXiv:2508.08250 for Wilson loops in Yang-Mills theories in AdS. Our proof is valid in general and applies, in particular, t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The defects are assumed to be conformal with boundary conditions that break bulk isometries in a manner compatible with the use of conformal symmetry to protect operator dimensions, without additional dynamical assumptions on the bulk theory.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Conformal defects in Anti-de Sitter space host a displacement operator whose dimension is fixed by residual symmetry, even when the boundary theory is non-local.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8a851aa0bb377309dce0df329b5d6a6ea80bcfeb6a7d0529a62f9030798c34cb"},"source":{"id":"2605.13947","kind":"arxiv","version":1},"verdict":{"id":"37dd47cb-e918-4186-901e-17634596696e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:46:57.385829Z","strongest_claim":"we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present.","one_line_summary":"Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The defects are assumed to be conformal with boundary conditions that break bulk isometries in a manner compatible with the use of conformal symmetry to protect operator dimensions, without additional dynamical assumptions on the bulk theory.","pith_extraction_headline":"Conformal defects in Anti-de Sitter space host a displacement operator whose dimension is fixed by residual symmetry, even when the boundary theory is non-local."},"references":{"count":65,"sample":[{"doi":"","year":null,"title":"A free theory example A simple example of a defect in a non-local CFT is obtained by coupling a generalized free field (GFF) ind dimensions to another GFF that lives on ap-dimensional linear subspace.","work_id":"1c0af973-6aa0-46a4-9619-2a5c09b2cb71","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The localized magnetic field in the long-range Ising model Starting from GFF, we can add an interaction term S0 = Z ddu 1 2 ϕSd 2∆ϕ ϕ+ λ 4! ϕ4 .(48) 12 If one takes ∆ ϕ = d−δ 4 , whereδis small, the i","work_id":"04b523a1-e030-4c34-be30-67e098a0fb65","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Yang-Mills Flux Tube in AdS,","work_id":"af8c18a5-7370-4fca-85a6-5fbd536ab522","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"C. G. Callan and F. Wilczek, Nuclear Physics B340, 366 (1990)","work_id":"e6437967-be18-4af9-9754-8d46bb896ece","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"The S-matrix Bootstrap I: QFT in AdS","work_id":"a6c147b9-25c8-4649-a69a-a4894db9167b","ref_index":5,"cited_arxiv_id":"1607.06109","is_internal_anchor":true}],"resolved_work":65,"snapshot_sha256":"95b2b632a8e559f63fe5b4a5989ff65095599cb37785c9d17003247897157746","internal_anchors":18},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}