{"paper":{"title":"Gauge-covariant Hadamard descent in Yang-Mills theory","arxiv_id":"2610.08515","primary_cat":"hep-th","submitted_at":"2026-10-06T15:17:58+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":0.65,"id":"s0","own":true,"role":"contribution","text":"We study the dimensional reduction of non-Abelian Yang-Mills theory from five to four dimensions.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.77,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.55,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.34,"limitation":0.0,"future_work":0.0,"contribution":0.65,"interpretation":0.0}},{"i":1,"p":0.88,"id":"s1","own":true,"role":"method","text":"In this framework, Hadamard descent is formulated as a restriction to gauge-equivalence classes that are invariant, up to gauge transformations, under translations along the reduced direction.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.58,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.88,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"The central result is that, prior to gauge fixing, the adjoint scalar of the reduced theory is not the connection component $A_u$ itself, but the gauge-covariant combination $\\widetilde{\\Phi}=\\epsilon-\\iota_YA$, which follows naturally from the covariant Cartan identity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.91,"quantitative":false,"quantitative_p":0.13,"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":3,"p":0.57,"id":"s3","own":true,"role":"interpretation","text":"The usual identification with $A_u$ is recovered, up to the sign convention adopted here, in the $u$-independent gauge, while global holonomy data remain additional information to be specified separately.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.77,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.42,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.57}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"result","text":"We show that the reduced theory takes the form of a Yang--Mills--Higgs theory with the Higgs field in the adjoint representation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":5,"p":0.91,"id":"s5","own":true,"role":"contribution","text":"As an example, we focus on the $U(2)$ gauge theory and analyze the Higgs mechanism, together with the associated symmetry breaking pattern, when the reduced theory is expanded around the ground state of the parent theory.","hedge":{"p":0.91,"label":"asserted"},"own_p":0.94,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.31,"role_probabilities":{"gap":0.0,"method":0.08,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.91,"interpretation":0.0}},{"i":6,"p":0.79,"id":"s6","own":true,"role":"result","text":"We then include fermions and show that, in the $u$-independent gauge, the extra-dimensional component of the gauge connection generates a pseudoscalar Yukawa coupling which, on the vacuum configuration, can be converted into a fermion mass term by a chiral field redefinition, while the gauge interaction remains vectorial.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.79,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.21,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"The central result is that, prior to gauge fixing, the adjoint scalar of the reduced theory is not the connection component $A_u$ itself, but the gauge-covariant combination $\\widetilde{\\Phi}=\\epsilon-\\iota_YA$, which follows naturally from the covariant Cartan identity.","location":"abstract s2","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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