{"paper":{"title":"Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models","arxiv_id":"2009.13588","primary_cat":"hep-th","submitted_at":"2020-09-28T19:08:51+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":1.0,"id":"s0","own":false,"role":"background","text":"In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition.","hedge":{"p":0.91,"label":"hedged_possibility"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"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":0.93,"id":"s1","own":false,"role":"gap","text":"However, understanding the phase diagram and finding fixed points under the renormalization group flow remains a major challenge.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.93,"method":0.0,"result":0.0,"background":0.07,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.81,"id":"s2","own":true,"role":"contribution","text":"In this work we tackle the issue for a tensorial group field theory using the functional renormalization group method.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.89,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.19,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.81,"interpretation":0.0}},{"i":3,"p":0.84,"id":"s3","own":true,"role":"method","text":"We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.84,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.16,"interpretation":0.0}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"result","text":"For a tensor field of rank $r$ on U$(1)$ we explicitly calculate beta functions and find equivalence with those of O$(N)$ models but with an effective dimension flowing from $r-1$ to zero.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.26,"quantitative":true,"quantitative_p":0.88,"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":0.96,"id":"s5","own":true,"role":"result","text":"In the $r-1$ dimensional regime, the equivalence to O$(N)$ models is modified by a tensor specific flow of the anomalous dimension with the consequence that the Wilson-Fisher type fixed point solution has two branches.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.04}},{"i":6,"p":0.81,"id":"s6","own":true,"role":"result","text":"However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.41,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.81,"background":0.0,"limitation":0.15,"future_work":0.0,"contribution":0.0,"interpretation":0.04}},{"i":7,"p":0.87,"id":"s7","own":false,"role":"future_work","text":"To overcome this limitation, it is necessary to go beyond compact configuration space.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.34,"main_claim_p":0.19,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.12,"future_work":0.87,"contribution":0.0,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":0.81,"text":"However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration.","location":"abstract s6","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":6289,"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":0.04,"states_limitation":0.97,"human_participants":0.01,"controlled_comparison":0.04,"randomized_assignment":0.01,"states_quantitative_result":0.45,"compares_with_prior_results":0.74,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.99,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.01,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.99,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.39,"text":"We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space.","location":"abstract s3"}},"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 v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":8,"sentences_in_abstract":8},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}