{"paper":{"title":"Where is the conformal coupling in Palatini gravity?","arxiv_id":"2610.16954","primary_cat":"gr-qc","submitted_at":"2026-10-12T15:23:22+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":0.94,"id":"s0","own":true,"role":"contribution","text":"We study the conformal coupling in the torsion-free Palatini formulation with an ordinary scalar kinetic term.","hedge":{"p":0.51,"label":"unclear"},"own_p":0.9,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.06,"limitation":0.0,"future_work":0.0,"contribution":0.94,"interpretation":0.0}},{"i":1,"p":0.99,"id":"s1","own":true,"role":"result","text":"Tuning the curvature coupling cannot restore Weyl invariance in a Palatini theory with an ordinary scalar kinetic term because, for an independent and inert connection, the scalar-curvature term is separately Weyl-invariant, and no finite curvature coupling cancels the Weyl variation of the kinetic term.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.7,"main_claim_p":0.82,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.01}},{"i":2,"p":0.88,"id":"s2","own":true,"role":"method","text":"This can be demonstrated by evaluating the energy-momentum trace on the scalar equation of motion and noting that it is explicitly independent of the Palatini coupling.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.86,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.88,"result":0.08,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.01}},{"i":3,"p":0.56,"id":"s3","own":true,"role":"result","text":"Eliminating the connection, we construct a map between the curvature coupling and the effective coupling for the equivalent metric theory, and demonstrate that the scalar continues to propagate even if the reduced kinetic coefficient vanishes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.56,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.31,"interpretation":0.0}},{"i":4,"p":0.9,"id":"s4","own":true,"role":"result","text":"We also show that it becomes a Weyl compensator with a scale-invariant potential only in the rescaled infinite-coupling limit, which in four dimensions is directly related to Palatini ${\\cal R}^2$ gravity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.79,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.9,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.08}},{"i":5,"p":0.93,"id":"s5","own":true,"role":"result","text":"We calculate the running of the couplings at one loop, and we find that the conformal shift in the metric-curvature coupling's beta function generates a metric-curvature coupling on a fixed metric-affine background, whereas the independent-curvature coupling runs homogeneously.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.56,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.93,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.0}},{"i":6,"p":0.51,"id":"s6","own":true,"role":"method","text":"Furthermore, we follow an alternate prescription in which the connection is allowed to respond to the scalar fluctuations, which results in a different scalar Hessian and therefore different beta functions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.51,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.0}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"result","text":"Nonetheless, we find that both prescriptions admit the formal infrared limit $(\\xi_{eff},\\lambda_{eff})\\to(1/6,0)$ through different limits of the original couplings in the case of positive perturbative quartics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.16,"quantitative":true,"quantitative_p":0.92,"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":8,"p":0.98,"id":"s8","own":true,"role":"result","text":"Finally, we note that trajectories starting on the positive gravitational branch encounter a vanishing gravitational coefficient at a finite scale before this endpoint.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.89,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":1.0,"text":"Tuning the curvature coupling cannot restore Weyl invariance in a Palatini theory with an ordinary scalar kinetic term because, for an independent and inert connection, the scalar-curvature term is separately Weyl-invariant, and no finite curvature coupling cancels the Weyl variation of the kinetic term.","location":"abstract s1","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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