{"paper":{"title":"Crosscap Defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Crosscap defects arise from Z2 quotients of spacetime and generalize CFT on real projective space to higher codimensions.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Anders Wallberg, Nadav Drukker, Shota Komatsu","submitted_at":"2026-04-21T18:00:01Z","abstract_excerpt":"We introduce a novel class of defects, termed crosscap defects, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a $Z_2$ automorphism, and provide higher-codimension generalisations of CFT on real projective space ($RP^{d}$). Crosscap defects extend along a $p$-dimensional fixed locus of the $Z_2$ action and preserve an $SO(p+1,1)\\times PO(d-p)$ subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several crosscap crossing "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a novel class of defects, termed crosscap defects, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a Z2 automorphism, and provide higher-codimension generalisations of CFT on real projective space (RP^d).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Z2 automorphism admits a p-dimensional fixed locus that preserves an SO(p+1,1)×PO(d-p) subgroup of the conformal group, allowing a consistent definition of the defect and its three OPE channels in general dimensions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Crosscap defects arise from Z2 quotients of spacetime and generalize CFT on real projective space to higher codimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2b85361b8924486d43f9c2671fd3d04020b9f0b2aa2573d84b22d10e9f557904"},"source":{"id":"2604.19868","kind":"arxiv","version":2},"verdict":{"id":"b15f23bd-f9b2-4b55-ab4e-18112dad6f95","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:33:48.659204Z","strongest_claim":"We introduce a novel class of defects, termed crosscap defects, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a Z2 automorphism, and provide higher-codimension generalisations of CFT on real projective space (RP^d).","one_line_summary":"Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Z2 automorphism admits a p-dimensional fixed locus that preserves an SO(p+1,1)×PO(d-p) subgroup of the conformal group, allowing a consistent definition of the defect and its three OPE channels in general dimensions.","pith_extraction_headline":"Crosscap defects arise from Z2 quotients of spacetime and generalize CFT on real projective space to higher codimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.19868/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":75,"sample":[{"doi":"","year":2019,"title":"The Conformal Bootstrap: Theory, Numerical Techniques, and Applications","work_id":"3458c84a-2848-4b87-8045-6bbc8c34f2ba","ref_index":1,"cited_arxiv_id":"1805.04405","is_internal_anchor":true},{"doi":"","year":2013,"title":"The bootstrap program for boundary CFTd","work_id":"57502a11-e7c5-459f-b71c-927b2ae90dcc","ref_index":2,"cited_arxiv_id":"1210.4258","is_internal_anchor":true},{"doi":"","year":2015,"title":"Boundary and interface CFTs from the conformal bootstrap","work_id":"9a3cc419-336d-48a2-875a-f7746d76d56f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Defects in conformal field theory","work_id":"d2c0255d-d451-4400-a489-ef3e46e9c8bd","ref_index":4,"cited_arxiv_id":"1601.02883","is_internal_anchor":true},{"doi":"","year":2018,"title":"The conformal bootstrap at finite temperature","work_id":"3424788b-39a4-45e1-bb1b-9b259949424c","ref_index":5,"cited_arxiv_id":"1802.10266","is_internal_anchor":true}],"resolved_work":75,"snapshot_sha256":"04dff23214141b7dad7a93be896d5560bdeb3e7d40c271d9194d731fe41c1390","internal_anchors":36},"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"}