{"paper":{"title":"Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings","arxiv_id":"1306.0002","primary_cat":"hep-th","submitted_at":"2013-05-31T20:00:00+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.97,"id":"s0","own":true,"role":"contribution","text":"We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.87,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":1,"p":0.73,"id":"s1","own":true,"role":"result","text":"The higher genus topological string amplitudes are expressed as polynomials in the generators of these rings, giving them a global description in the moduli space.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.25,"interpretation":0.0}},{"i":2,"p":0.96,"id":"s2","own":true,"role":"result","text":"At particular loci, the amplitudes yield the generating functions of Gromov-Witten invariants.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.5,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.02}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"result","text":"We show that these rings are isomorphic to the rings of quasi modular forms for threefolds with duality groups for which these are known.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.33,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.72,"id":"s4","own":true,"role":"result","text":"For the other cases, they provide generalizations thereof.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.65,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.72,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.23,"interpretation":0.05}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"contribution","text":"We furthermore study an involution which acts on the quasi modular forms.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.93,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"interpretation","text":"We interpret it as a duality which exchanges two distinguished expansion loci of the topological string amplitudes in the moduli space.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.88,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}},{"i":7,"p":0.75,"id":"s7","own":true,"role":"contribution","text":"We construct these special polynomial rings and match them with known quasi modular forms for non-compact Calabi-Yau geometries and their mirrors including local P^2 and local del Pezzo geometries with E_5,E_6,E_7 and E_8 type singularities.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.22,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.24,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.0}},{"i":8,"p":0.84,"id":"s8","own":true,"role":"contribution","text":"We provide the analogous special polynomial ring for the quintic.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.16,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.84,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.81,"text":"We show that these rings are isomorphic to the rings of quasi modular forms for threefolds with duality groups for which these are known.","location":"abstract 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