{"paper":{"title":"Superconformal index with surface defects for class ${\\cal S}_k$","arxiv_id":"1606.01653","primary_cat":"hep-th","submitted_at":"2016-06-06T08:26:40+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":0.54,"id":"s0","own":false,"role":"background","text":"We study surface defects in 4d $\\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at $\\mathbb{C}^2/\\mathbb{Z}_k$ singularities, compactified on Riemann surfaces with punctures.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.31,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.54,"limitation":0.0,"future_work":0.0,"contribution":0.46,"interpretation":0.0}},{"i":1,"p":0.63,"id":"s1","own":true,"role":"method","text":"First we apply a method based on Riemann surface description and obtain the superconformal index of the theories in the presence of surface defects labelled by arbitrary symmetric representations of $su(N)$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.63,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.35,"interpretation":0.0}},{"i":2,"p":0.72,"id":"s2","own":true,"role":"method","text":"Then we propose another description for the same surface defects, which involves 4d-2d coupled systems, by identifying which 2d $\\mathcal{N}=(0,2)$ theories should be coupled.","hedge":{"p":0.88,"label":"asserted"},"own_p":0.9,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.72,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.28,"interpretation":0.0}},{"i":3,"p":0.84,"id":"s3","own":true,"role":"result","text":"We compute the index of the 4d-2d systems and reproduce the results obtained from the first method.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.22,"quantitative":false,"quantitative_p":0.25,"role_probabilities":{"gap":0.0,"method":0.09,"result":0.84,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":4,"p":0.89,"id":"s4","own":true,"role":"contribution","text":"Finally we study the 2d TQFT structure of the index for class $\\mathcal{S}_{k}$ theories by obtaining several eigenfunctions and eigenvalues of the difference operators that capture the surface defects and checking their relation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.08,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.89,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.81,"text":"We compute the index of the 4d-2d systems and reproduce the results obtained from the first method.","location":"abstract s3","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":4605,"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":0.06,"states_limitation":0.06,"human_participants":0.01,"controlled_comparison":0.04,"randomized_assignment":0.01,"states_quantitative_result":0.07,"compares_with_prior_results":0.84,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.98,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.98,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.02}},"contribution_type":{"p":0.96,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.04,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.96,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.85,"text":"Then we propose another description for the same surface defects, which involves 4d-2d coupled systems, by identifying which 2d $\\mathcal{N}=(0,2)$ theories should be coupled.","location":"abstract s2"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":5,"sentences_in_abstract":5},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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