{"paper":{"title":"Discrete Gauge Anomalies and Instantons","arxiv_id":"2405.09007","primary_cat":"hep-th","submitted_at":"2024-05-15T00:18:06+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":0.65,"id":"s0","own":true,"role":"background","text":"We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly.","hedge":{"p":0.66,"label":"asserted"},"own_p":0.67,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.65,"limitation":0.0,"future_work":0.0,"contribution":0.35,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $\\pi_4(Sp(k))=\\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\\pi_3(G)=\\mathbb{Z}$, via the fermion zero mode counting.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.7,"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":2,"p":0.56,"id":"s2","own":true,"role":"result","text":"We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.53,"main_claim_p":0.15,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.56,"background":0.06,"limitation":0.0,"future_work":0.0,"contribution":0.32,"interpretation":0.05}},{"i":3,"p":0.86,"id":"s3","own":false,"role":"gap","text":"This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead.","hedge":{"p":0.76,"label":"unclear"},"own_p":0.26,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.86,"method":0.0,"result":0.0,"background":0.04,"limitation":0.0,"future_work":0.06,"contribution":0.03,"interpretation":0.01}},{"i":4,"p":0.59,"id":"s4","own":true,"role":"result","text":"After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.36,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.59,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.38,"interpretation":0.0}},{"i":5,"p":0.74,"id":"s5","own":true,"role":"result","text":"We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.81,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.74,"background":0.0,"limitation":0.0,"future_work":0.01,"contribution":0.23,"interpretation":0.02}}]},"compiled":{"main_claim":{"p":0.99,"text":"After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra.","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 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