{"paper":{"title":"Algebra of the infrared and secondary polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.AT","math.DG"],"primary_cat":"math.SG","authors_text":"Maxim Kontsevich, Mikhail Kapranov, Yan Soibelman","submitted_at":"2014-08-12T09:22:15Z","abstract_excerpt":"We study algebraic structures ($L_\\infty$ and $A_\\infty$-algebras) introduced by Gaiotto, Moore and Witten in their recent work devoted to certain supersymmetric 2-dimensional massive field theories.\n  We show that such structures can be systematically produced in any number of dimensions by using the geometry of secondary polytopes, esp. their factorization properties. In particular, in 2 dimensions, we produce, out of a polyhedral \"coefficient system\", a dg-category $R$ with a semi-orthogonal decomposition and an $L_\\infty$-algebra $\\mathfrak g$. We show that $\\mathfrak g$ is quasi-isomorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2673","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":""},"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"}