{"paper":{"title":"Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Christoph Nega, Claude Duhr, Florian Loebbert, Franziska Porkert","submitted_at":"2022-09-12T14:50:03Z","abstract_excerpt":"We argue that $\\ell$-loop Yangian-invariant fishnet integrals in 2 dimensions are connected to a family of Calabi-Yau $\\ell$-folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators provide its Picard-Fuchs differential ideal. Using mirror symmetry, we can identify the value of the integral as the quantum volume of the mirror Calabi-Yau. We find that, similar to what happens in string theory, for $\\ell=1$ and 2 the value of the integral agrees with the classical volume of the mirror, but starting from $\\ell=3$, the classical volume gets "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05291","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.05291/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}