{"paper":{"title":"On the Algebra of the Infrared with Twisted Masses","arxiv_id":"2408.08372","primary_cat":"hep-th","submitted_at":"2024-08-15T18:32:45+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-1.13.0 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 v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The Algebra of the Infrared \\cite{Gaiotto:2015aoa} is a framework to construct local observables, interfaces, and categories of supersymmetric boundary conditions of massive $\\mathcal{N}=(2,2)$ theories in two dimensions by using information only about the BPS sector.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.21,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.87,"id":"s1","own":true,"role":"contribution","text":"The resulting framework is known as the ``web-based formalism.'' In this paper we initiate the generalization of the web-based formalism to include a much wider class of $\\mathcal{N}=(2,2)$ quantum field theories than was discussed in \\cite{Gaiotto:2015aoa}: theories with non-trivial twisted masses.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.59,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.35,"role_probabilities":{"gap":0.07,"method":0.0,"result":0.0,"background":0.06,"limitation":0.0,"future_work":0.0,"contribution":0.87,"interpretation":0.0}},{"i":2,"p":0.75,"id":"s2","own":false,"role":"contribution","text":"The essential new ingredient is the presence of BPS particles within a fixed vacuum sector.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.18,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.08,"method":0.13,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.01}},{"i":3,"p":0.87,"id":"s3","own":true,"role":"contribution","text":"In this paper we work out the web-based formalism for the simplest class of theories that allow for such BPS particles: theories with a single vacuum and a single twisted mass.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.91,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.84,"role_probabilities":{"gap":0.0,"method":0.07,"result":0.0,"background":0.0,"limitation":0.06,"future_work":0.0,"contribution":0.87,"interpretation":0.0}},{"i":4,"p":1.0,"id":"s4","own":true,"role":"result","text":"We show that even in this simple setting there are interesting new phenomenon including the emergence of Fock spaces of closed solitons and a natural appearance of Koszul dual algebras.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.43,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.6,"id":"s5","own":false,"role":"interpretation","text":"Mathematically, studying theories with twisted masses includes studying the Fukaya-Seidel category of A-type boundary conditions for Landau-Ginzburg models defined by a closed holomorphic one-form.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.17,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.01,"background":0.29,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.6}},{"i":6,"p":0.92,"id":"s6","own":true,"role":"contribution","text":"This paper sketches a web-based construction for the category of A-type boundary conditions for one-forms with a single Morse zero and a single non-trivial period.","hedge":{"p":0.81,"label":"asserted"},"own_p":0.85,"main_claim_p":0.1,"quantitative":true,"quantitative_p":0.73,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.01,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.92,"interpretation":0.0}},{"i":7,"p":0.79,"id":"s7","own":true,"role":"contribution","text":"We demonstrate our formalism explicitly in a particularly instructive example.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.19,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.79,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.97,"text":"We show that even in this simple setting there are interesting new phenomenon including the emergence of Fock spaces of closed solitons and a natural appearance of Koszul dual algebras.","location":"abstract s4","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":6508,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.24,"states_limitation":0.58,"human_participants":0.01,"controlled_comparison":0.03,"randomized_assignment":0.01,"states_quantitative_result":0.04,"compares_with_prior_results":0.81,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":0.98,"value":"proof or derivation","probabilities":{"argument":0.02,"literature":0.0,"proof_or_derivation":0.98,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.81,"value":"method or tool","probabilities":{"review":0.0,"method_or_tool":0.81,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.19,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.9,"text":"The resulting framework is known as the ``web-based formalism.'' 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