{"paper":{"title":"On exact correlation functions of chiral ring operators in $2d$ $\\mathcal{N}=(2, 2)$ SCFTs via localization","arxiv_id":"1712.01164","primary_cat":"hep-th","submitted_at":"2017-12-04T15:57:41+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 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 v2","sentences":[{"i":0,"p":0.97,"id":"s0","own":true,"role":"contribution","text":"We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in $\\mathcal{N}=(2, 2)$ superconformal field theories (SCFTs) with central charge $c\\geq 3$, especially for SCFTs with Calabi-Yau geometric phases.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.92,"main_claim_p":0.15,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":1,"p":0.59,"id":"s1","own":true,"role":"method","text":"We extend the method in arXiv:1602.05971 with mild modifications, so that it is applicable to disentangle operators mixing on $S^2$ in nilpotent (twisted) chiral rings of $2d$ SCFTs.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.9,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.32,"role_probabilities":{"gap":0.0,"method":0.59,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.41,"interpretation":0.0}},{"i":2,"p":0.89,"id":"s2","own":true,"role":"result","text":"With the extended algorithm and technique of localization, we compute exactly the extremal correlators in $2d$ $\\mathcal{N}=(2, 2)$ (twisted) chiral rings as non-holomorphic functions of marginal parameters of the theories.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.63,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.89,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"interpretation","text":"Especially in the context of Calabi-Yau geometries, we give an explicit geometric interpretation to our algorithm as the Griffiths transversality with projection on the Hodge bundle over Calabi-Yau complex moduli.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.15,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.98}},{"i":4,"p":0.74,"id":"s4","own":true,"role":"contribution","text":"We also apply the method to compute extremal correlators in K\\\"{a}hler moduli, or say twisted chiral rings, of several interesting Calabi-Yau manifolds.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.26,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.74,"interpretation":0.0}},{"i":5,"p":0.71,"id":"s5","own":true,"role":"contribution","text":"In the case of complete intersections in toric varieties, we provide an alternative formalism for extremal correlators via localization onto Higgs branch.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.28,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.71,"interpretation":0.0}},{"i":6,"p":0.95,"id":"s6","own":true,"role":"result","text":"In addition, as a spinoff we find that, from the extremal correlators of the top element in twisted chiral rings, one can extract chiral correlators in A-twisted topological theories.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.95,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":1.0,"text":"With the extended algorithm and technique of localization, we compute exactly 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